Q&A Hero

Q: Which of the following is not one of the guidelines for including/excluding variables in a regression equation? a. Look at t-value and associated p-value b. Check whether t-value is less than or greater than 1.0 c. Variables are logically related to one another d. Use economic or physical theory to make decision e. All of these options are guidelines

Q: Suppose you run a regression of a person's height on his/her right and left foot sizes, and you suspect that there may be multicollinearity between the foot sizes. What types of problems might you see if your suspicions are true? a. "Wrong" values for the coefficients for the left and right foot size b. Large p-values for the coefficients for the left and right foot size c. Small t-values for the coefficients for the left and right foot size d. All of these options

Q: The appropriate hypothesis test for an ANOVA test is: a. b. c. d.

Q: The test statistic in an ANOVA analysis is: a. the t-statistic b. the z-statistic c. the F-statistic d. the Chi-square statistic

Q: In regression analysis, the ANOVA table analyzes: a. the variation of the response variable Y b. the variation of the explanatory variable X c. the total variation of all variables d. All of these options

Q: The ANOVA table splits the total variation into two parts. They are the a. acceptable and unacceptable variation b. adequate and inadequate variation c. resolved and unresolved variation d. explained and unexplained variation

Q: The appropriate hypothesis test for a regression coefficient is: a. b. c. d. None of these options

Q: The value k in the number of degrees of freedom, n-k-1, for the sampling distribution of the regression coefficients represents: a. the sample size b. the population size c. the number of coefficients in the regression equation, including the constant d. the number of independent variables included in the equation

Q: In the standardized value , the symbol represents the: a. mean of b. variance of c. standard error of d. degrees of freedom of

Q: The t-value for testing is calculated using which of the following equations: a. n " k - 1 b. c. d.

Q: Which of the following is the relevant sampling distribution for regression coefficients? a. Normal distribution b. t-distribution with n-1 degrees of freedom c. t-distribution with n-1-k degrees of freedom d. F-distribution with n-1-k degrees of freedom

Q: Which of the following definitions best describes parsimony? a. Explaining the most with the least b. Explaining the least with the most c. Being able to explain all of the change in the response variable d. Being able to predict the value of the response variable far into the future

Q: A scatterplot that exhibits a "fan" shape (the variation of Y increases as X increases) is an example of: a. homoscedasticity b. heteroscedasticity c. autocorrelation d. multicollinearity

Q: Time series data often exhibits which of the following characteristics? a. homoscedasticity b. heteroscedasticity c. autocorrelation d. multicollinearity

Q: Another term for constant error variance is: a. homoscedasticity b. heteroscedasticity c. Autocorrelation d. multicollinearity

Q: In regression analysis, multicollinearity refers to: a. the response variables being highly correlated b. the explanatory variables being highly correlated c. the response variable(s) and the explanatory variable(s) are highly correlated with one another d. the response variables are highly correlated over time.

Q: The term autocorrelation refers to: a. analyzed data refers to itself b. sample is related too closely to the population c. data are in a loop (values repeat themselves) d. time series variables are usually related to their own past values

Q: Which of the following is true regarding regression error, e a. it is the same as a residual b. it can be calculated from the observed data c. it cannot be calculated from the observed data d. it is unbiased

Q: The error term represents the vertical distance from any point to the a. estimated regression line b. population regression line c. value of the Y's d. mean value of the X's

Q: Which of the following is not one of the assumptions of regression? a. There is a population regression line b. The response variable is normally distributed c. The standard deviation of the response variable increases as the explanatory variables increase d. The errors are probabilistically independent

Q: Suggest an alternative model to address the issues identified in Question 131. Are you able to obtain an improved fit to the data? Explain your answer.

Q: Diagnose what may be causing the problem seen in the residuals plot in Question 130. What issue(s) do you identify?

Q: Plot the fitted values versus residuals associated with the model in Question 128. What does the plot indicate?

Q: Perform an F-test for the existence of a linear relationship between Y and X. Use a 5% level of significance.

Q: NARRBEGIN: SA_128_132A sporting goods store would like to determine what relationship exists between their annual advertising budget (Y) and the annual sales (X) so that they can assess the effectiveness of their current channels. The data for the last five years is provided in the table below (in $000).NARREND(A) Estimate a simple linear regression model using the sample data. How well does the estimated model fit the sample data?(B) Perform an F-test for the existence of a linear relationship between Y and X. Use a 5% level of significance.(C) Plot the fitted values versus residuals associated with the model in (A). What does the plot indicate?(D) Diagnose what may be causing the problem seen in the residuals plot in (C). What issue(s) do you identify?(E) Suggest an alternative model to address the issues identified in (D). Are you able to obtain an improved fit to the data? Explain your answer.

Q: Do you see any problems evident in the plot below of residuals versus fitted values from a multiple regression analysis? Explain your answer.

Q: NARRBEGIN: SA_124_126The manager of a commuter rail transportation system was recently asked by his governing board to predict the demand for rides in the large city served by the transportation network. The system manager has collected data on variables thought to be related to the number of weekly riders on the city's rail system. The table shown below contains these data.The variables "weekly riders" and "population" are measured in thousands, and the variables "price per ride", "income", and "parking rate" are measured in dollars.NARREND(A) Estimate a multiple regression model using all of the available explanatory variables.(B) Conduct and interpret the result of an F- test on the given model. Employ a 5% level of significance in conducting this statistical hypothesis test.(C) Is there evidence of autocorrelated residuals in this model? Explain why or why not.

Q: NARRBEGIN: SA_119_123A manufacturing firm wants to determine whether a relationship exists between the number of work-hours an employee misses per year (Y) and the employee's annual wages (X), to test the hypothesis that increased compensation induces better work attendance. The data provided in the table below are based on a random sample of 15 employees from this organization.NARREND(A) Estimate a simple linear regression model using the sample data. How well does the estimated model fit the sample data?(B) Perform an F-test for the existence of a linear relationship between Y and X. Use a 5% level of significance.(C) Plot the fitted values versus residuals associated with the model in Question 119. What does the plot indicate?(D) How do you explain the results you have found in (A) through (C)?(E) Suppose you learn that the 10th employee in the sample has been fired for missing an excessive number of work-hours during the past year. In light of this information, how would you proceed to estimate the relationship between the number of work-hours an employee misses per year and the employee's annual wages, using the available information? If you decide to revise your estimate of this regression equation, repeat (A) and (B)

Q: NARRBEGIN: SA_114_118Many companies manufacture products that are at least partially produced using chemicals (for example, paint). In many cases, the quality of the finished product is a function of the temperature and pressure at which the chemical reactions take place. Suppose that a particular manufacturer in Texas wants to model the quality (Y) of a product as a function of the temperature and the pressure at which it is produced. The table below contains data obtained from a designed experiment involving these variables. Note that the assigned quality score can range from a minimum of 0 to a maximum of 100 for each manufactured product.NARREND(A) Estimate a multiple regression model that includes the two given explanatory variables. Assess this set of explanatory variables with an F-test, and report a p-value.(B) Conduct a partial F-test to decide whether it is worthwhile to add second-order terms (i.e.,) to the multiple regression equation estimated in Question 114. Employ a 5% significance level in conducting this hypothesis test.(C) Identify and interpret the percentage of variance explained for the model in (A).(D) Identify and interpret the percentage of variance explained for the model in (B).(E) Which regression equation is the most appropriate one for modeling the quality of the given product? Bear in mind that a good statistical model is usually parsimonious.

Q: NARRBEGIN: SA_103_113The owner of a large chain of health spas has selected eight of her smaller clubs for a test in which she varies the size of the newspaper ad , and the amount of the initiation fee discount to see how this might affect the number of prospective members who visit each club during the following week. The results are shown in the table below:ClubNew Visitors (Y)Ad Column Inches ()Discount Amount ()1234$100230720320340426625520250618530717425831880The results of a multiple regression analysis are below.NARREND(A) Determine the least-squares multiple regression equation.(B) Interpret the Y- intercept of the regression equation.(C) Interpret the partial regression coefficients.(D) What is the estimated number of new visitors to a club if the size of the ad is 6 column-inches and a $100 discount is offered?(E) Determine the approximate 95% prediction interval for the number of new visitors to a given club when the ad is 5 column-inches and the discount is $80.(F) What is the value for the percentage of variation explained, and exactly what does it indicate?(G) At the 0.05 level, is the overall regression equation in (A) significant?(H) Use the 0.05 level in concluding whether each partial regression coefficient differs significantly from zero.(I Interpret the results of the preceding tests in (H) and (I) in the context of the two explanatory variables described in the problem.(J) Construct a 95% confidence interval for each partial regression coefficient in the population regression equation.

Q: NARRBEGIN: SA_100_102A new online auction site specializes in selling automotive parts for classic cars. The founder of the company believes that the price received for a particular item increases with its age (i.e., the age of the car on which the item can be used in years) and with the number of bidders. The Excel multiple regression output is shown below.Summary measuresMultiple R0.8391R-Square0.7041Adj R-Square0.6783StErr of Estimate148.828ANOVA TableSourcedfSSMSFp-valueExplained21212039606019.727.36010Unexplained23509444.922149.8Regression coefficientsCoefficientStd Errt-valuep-valueConstant-1242.99331.204-3.75290.001Age of Item75.01710.657.04590Number of Bidders13.97310.441.3380.194NARREND(A) Estimate a multiple regression model for the data.(B) Which of the variables in this model have regression coefficients that are statistically different from 0 at the 5% significance level?(C) Given your findings in (B), which variables, if any, would you choose to remove from the model estimated in (A)? Explain your decision.

Q: Interpret the model you developed in Question 139. Does it help you assess the agency's claim? What should the agency conclude about the relationship between service interval and maintenance costs?

Q: Use what you have learned about transformations to fit an alternative model to the one in Question 135.

Q: Obtain a scatterplot of Maintenance Cost vs. Service Interval. Does this affect your opinion of the validity of the model in Question 135?

Q: Obtain a residual plot vs. Service Interval. Does this affect your opinion of the validity of the model in Question 135?

Q: Do you think this model proves the agency's point about maintenance? Explain your answer.

Q: NARRBEGIN: SA_135_140Adjustors working for a large insurance agency are each given a company car which they use on the job to travel to client locations to inspect damage to homes and automobiles that are covered by the agency. Although the cars are owned by the agency, maintenance is currently left up to the discretion of the adjustors, who are reimbursed for any costs they report. The agency believes that the lack of a maintenance policy has led to unnecessary maintenance expenses. In particular, they believe that many agents wait too long to have maintenance performed on their company cars, and that in such cases, maintenance expenses are inordinately high. The agency recently conducted a study to investigate the relationship between the reported cost of maintenance visits for their company cars (Y) and the length of time since the last maintenance service (X). The sample data are shown below:NARREND(A) Estimate a simple linear regression model with Service Interval (X) and Maintenance Cost (Y). Interpret the slope coefficient of the least squares line as well as the computed value of.(B) Do you think this model proves the agency's point about maintenance? Explain your answer.(C) Obtain a residual plot vs. Service Interval. Does this affect your opinion of the validity of the model in (A)?(D) Obtain a scatterplot of Maintenance Cost vs. Service Interval. Does this affect your opinion of the validity of the model in (A)?(E) Use what you have learned about transformations to fit an alternative model to the one in (A).(F) Interpret the model you developed in (E). Does it help you assess the agency's claim? What should the agency conclude about the relationship between service interval and maintenance costs?

Q: NARRBEGIN: SA_129_134An express delivery service company recently conducted a study to investigate the relationship between the cost of shipping a package (Y), the package weight, and the distance shipped . Twenty packages were randomly selected from among the large number received for shipment, and a detailed analysis of the shipping cost was conducted for each package. The sample information is shown in the table below:NARREND(A) Estimate a simple linear regression model involving shipping cost and package weight. Interpret the slope coefficient of the least squares line as well as the computed value of.(B) Add another explanatory variable - distance shipped " to the regression to (A). Estimate and interpret this expanded model. How does the value for this multiple regression model compare to that of the simple regression model estimated in (A)? Explain any difference between the two values. Compute and interpret the adjusted value for the revised model.(C) Suppose that one of the managers of this express delivery service company is trying to decide whether to add an interaction term involving the package weight and the distance shipped in the multiple regression model developed previously. Why would the manager want to add such a term to the regression equation?(D) Estimate the revised model using the interaction term suggested in (C).(E) Interpret each of the estimated coefficients in your revised model in (D). In particular, how do you interpret the coefficient for the interaction term in the revised model?(F) Does this revised model in (D) fit the given data better than the original multiple regression model in (B)? Explain why or why not.

Q: NARRBEGIN: SA_124_128A new online auction site specializes in selling automotive parts for classic cars. The founder of the company believes that the price received for a particular item increases with its age (i.e., the age of the car on which the item can be used in years) and with the number of bidders. The multiple regression output is shown below.Summary measuresMultiple R0.8391R-Square0.7041Adj R-Square0.6783StErr of Estimate148.828Regression coefficientsCoefficientStd Errt-valuep-valueConstant-1242.986331.204-3.75290.001Age of part75.01710.6477.04590Number of Bidders13.97310.4431.3380.194NARREND(A) Use the information above to estimate the linear regression model.(B) Interpret each of the estimated regression coefficients of the regression model in (A).(C) Identify and interpret the coefficient of determination () for the model in (A).(D) Identify and interpret the standard error of the estimate (se) for the model in (A).(E) Would you recommend that this company examine any other factors to predict the selling price? If yes, what other factors would you want to consider? Explain your answer.

Q: NARRBEGIN: SA_119_123A realtor in a local area is interested in being able to predict the selling price for a newly listed home or for someone considering listing their home. This realtor would like to attempt to predict the selling price by using the size of the home (, in hundreds of square feet), the number of rooms (), the age of the home (, in years) and if the home has an attached garage (). Use the output below to determine if this realtor will be able to use this information to predict the selling price (in $1000).Summary measuresMultiple R0.9439R-Square0.891Adj. R-Square0.8474StErr of Estimate22.241Regression coefficientsCoefficientStd Errt-valuep-valueConstant-19.02654.769-0.34740.7355Size7.4941.5294.9010.0006Number of Rooms7.1539.2110.77670.4553Age-0.6730.992-0.67890.5126Attached Garage0.45320.1920.02240.9826NARREND(A) Use the information above to estimate the linear regression model.(B) Interpret each of the estimated regression coefficients of the regression model in (A).(C) Would any of the variables in this model be considered a dummy variable? Explain your answer.(D) Identify and interpret the coefficient of determination () and the standard error of the estimate (se) for the model in (A).(E) Use the estimated model in (A) to predict the sales price of a 2500 square feet, 15-year old house that has 5 rooms and an attached garage.

Q: NARRBEGIN: SA_114_118The human resource manager at Gamma, Inc. wants to examine the relationship between annual salaries (Y), the number of years employees have worked at Gamma, Inc. () and whether the employee is male or female (). They are also interested in whether the interaction between the two explanatory variables () has a significant impact on salaries. These data have been collected for a sample of 28 employees and the regression output is shown below.Summary measuresMultiple R0.8065R-Square0.6504Adj R-Square0.6067StErr of Estimate6572.3Regression coefficientsCoefficientStd Errt-valuep-valueConstant29831.683904.567.640Years Employed869.04266.783.2580.0033Gender-2396.544620.04-0.5190.6087Years & Gender403.93350.381.1530.2603NARREND(A) Use the information above to estimate the linear regression model.(B) Write the regression equation in (A) as two separate equations; one for females and one for males, and interpret the results.(C) Would any of the variables in the linear regression model in (A) be considered a dummy variable? Explain your answer.(D) Identify and interpret the coefficient of determination () for the model in (A).(E) Identify and interpret the standard error of estimate (se) for the model in (A).

Q: NARRBEGIN: SA_110_113The station manager of a local television station is interested in predicting the amount of television (in hours) that people will watch in the viewing area. The explanatory variables are: age (in years), education (highest level obtained, in years) and family size (number of family members in household). The multiple regression output is shown below:Summary measuresMultiple R0.844R-Square0.7123Adj R-Square0.6644StErr of Estimate0.5598ANOVA TableSourcedfSSMSFp-valueExplained313.96824.656114.85640Unexplained185.64130.3134Regression coefficientsCoefficientStd Errt-valuep-valueConstant1.6831.16961.43890.1674Age-0.04980.0199-2.50180.0222Education0.21350.05034.24260.0005Family Size0.04050.07840.51680.6116NARREND(A) Use the information above to estimate the linear regression model.(B) Interpret each of the estimated regression coefficients of the regression model in (A).(C) Identify and interpret the coefficient of determination () for the model in (A).(D) Identify and interpret the standard error of the estimate for the model in (A).

Q: NARRBEGIN: SA_107_109A large auto dealership is interested in determining the number of cars that will be sold in a given quarter. The management of the dealership believes that a relationship can be found between the number of cars sold (Y), the advertised price () and the current interest rates (). Their past experience shows that they tend to have better luck using a non-linear relationship. Below is the output from a regression analysis using the natural logarithm of the variables in the model.Summary measures Multiple R0.9326 R-Square0.8698 Adj R-Square0.8498 StErr of Estimate0.0259 ANOVA Table SourcedfSSMSFp-valueExplained20.05810.029043.41870.0000Unexplained130.00870.0007 Regression coefficients CoefficientStd Errt-valuep-value Constant4.39650.75495.82390.0001 Log Price-0.82550.24673.34560.0053 Log Interest-0.12250.1880-0.65120.5262 NARREND(A) Use the information above to estimate the regression model.(B) Interpret each of the estimated regression coefficients of the regression model in (A).(C) Does using a non-linear model seem to be a good choice in this example? Explain your answer.

Q: NARRBEGIN: SA_103_106La Cabaa, a popular motel chain in the southwest, is interested in developing a regression model that can predict the occupancy rate (%) of its motels. Currently, the company is interested in using two explanatory variables to predict occupancy. They want to use the amount of advertising (in $) used by each motel and if the particular location a franchised location. Some regression information is presented below:Summary measures Multiple R0.5358 R-Square0.2871 Adj R-Square0.2223 StErr of Estimate7.582 Regression coefficients CoefficientStd Errt-valuep-valueConstant43.11811.42633.77350.0010Advertising0.0013 0.00062.41190.0247Franchise3.038 3.17590.95670.3491NARREND(A) Use the information above to estimate the linear regression model.(B) Interpret each of the estimated regression coefficients of the regression model in (A).(C) Would any of the variables in this model be considered a dummy variable? Explain your answer.(D) Identify and interpret the coefficient of determination () and the standard error of the estimate (se) for the model in (A).

Q: NARRBEGIN: SA_98_102An automobile rental company wants to predict the yearly maintenance expense (Y) for an automobile using the number of miles driven during the year () and the age of the car (, in years) at the beginning of the year. The company has gathered the data on 10 automobiles and run a regression analysis with the results shown below:.Summary measures Multiple R0.9689 R-Square0.9387 Adj R-Square0.9212 StErr of Estimate72.218 Regression coefficients CoefficientStd Errt-valuep-valueConstant33.79648.1810.70140.5057Miles Driven0.05490.01912.86660.0241Age of car21.46720.5731.04340.3314NARREND(A) Use the information above to estimate the linear regression model.(B) Interpret each of the estimated regression coefficients of the regression model in (A).(C) Identify and interpret the coefficient of determination (), for the model in (A).(D) Identify and interpret the adjusted for the model in (A).

Q: NARRBEGIN: SA_91_97The information below represents the relationship between the selling price (Y, in $1000) of a home, the square footage of the home (), and the number of bedrooms in the home (). The data represents 65 homes sold in a particular area of a city and was analyzed using simple linear regression for each independent variable.Summary measures Multiple R0.8148 R-Square0.6640 StErr of Estimate8.5572 Regression coefficients CoefficientStd Errt-valuep-valueConstant52.1577.4784 6.97440.0000Square Footage 4.6460.416411.15750.0000Summary measures Multiple R0.6487 R-Square0.4208 StErr of Estimate11.2344 Regression coefficients CoefficientStd Errt-valuep-valueConstant100.6285.232419.23160.0000Number of Bedrooms11.0351.6310 6.76600.0000NARREND(A) Is there evidence of a linear relationship between the selling price and the square footage of the homes? If so, interpret the least squares line and characterize the relationship (i.e., positive, negative, strong, weak, etc.).(B) Identify and interpret the coefficient of determination () for the model in (A).(C) Identify and interpret the standard error of estimate for the model in (A).(D) Is there evidence of a linear relationship between the selling price and number of bedrooms of the homes? If so, interpret the least squares line and characterize the relationship (i.e., positive, negative, strong, weak, etc.).(E) Identify and interpret the coefficient of determination () for the model in (D).(F) Identify and interpret the standard error of the estimate () for the model in (C).(G) Which of the two variables, the square footage or the number of bedrooms, is the relationship with home selling price stronger? Justify your choice.

Q: NARRBEGIN: SA_82_90The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal "sized stores is selected, with the following results:StoreShelf Space XWeekly Sales Y1102.02102.63101.84152.35152.86153.07202.78203.19203.210253.011253.312253.5NARREND(A) Draw a scatterplot,of the data and comment on the relationship between shelf space and weekly sales.(B) Run a regression on this data set and report the results.(C) What are the least squares regression coefficients of the Y-intercept (a)and slope (b)?(D) Interpret the meaning of the slope b.(E) Predict the average weekly sales (in hundreds of dollars) of international food for stores with 13 feet of shelf space for international food.(F) Why would it not be appropriate to predict the average weekly sales (in hundreds of dollars) of international food for stores with 35 feet of shelf space for international food?(G) Identify the coefficient of determination,, and interpret its meaning.(H) Determine the standard error of the estimate. What does it represent?(I) Draw a scatterplot of residuals versus fitted values. What does this graph indicate?

Q: A constant elasticity, or multiplicative, model the dependent variable is expressed as a product of explanatory variables raised to powers

Q: A logarithmic transformation of the response variable Y is often useful when the distribution of Y is symmetric.

Q: The effect of a logarithmic transformation on a variable that is skewed to the right by a few large values is to "squeeze" the values together and make the distribution more symmetric

Q: The coefficients for logarithmically transformed explanatory variables should be interpreted as the percent change in the dependent variable for a 1% percent change in the explanatory variable.

Q: If a scatterplot of residuals shows a parabola shape, then a logarithmic transformation may be useful in obtaining a better fit

Q: The primary purpose of a nonlinear transformation is to "straighten out" the data on a scatterplot

Q: In a nonlinear transformation of data, the Y variable or the X variables may be transformed, but not both.

Q: If the regression equation includes anything other than a constant plus the sum of products of constants and variables, the model will not be linear

Q: We should include an interaction variable in a regression model if we believe that the effect of one explanatory variable on the response variable Y depends on the value of another explanatory variable.

Q: An interaction variable is the product of an explanatory variable and the dependent variable.

Q: If a categorical variable is to be included in a multiple regression, a dummy variable for each category of the variable should be used, but the original categorical variables should not be sued.

Q: The adjusted R2 is used primarily to monitor whether extra explanatory variables really belong in a multiple regression model

Q: The adjusted R2 is adjusted for the number of explanatory variables in a regression equation, and it has he same interpretation as the standard R2.

Q: The R2 can only increase when extra explanatory variables are added to a multiple regression model

Q: In a multiple regression analysis with three explanatory variables, suppose that there are 60 observations and the sum of the residuals squared is 28. The standard error of estimate must be 0.7071.

Q: For the multiple regression model , if were to increase by 5 units, holding and constant, the value of Y would be expected to decrease by 50 units.

Q: In the multiple regression model we interpret X1 as follows: holdingX2 constant, if X1 increases by 1 unit, then the expected value of Y will increase by 9 units.

Q: In a multiple regression problem with two explanatory variables if, the fitted regression equation is , then the estimated value of Y when and is 49.4.

Q: In a simple linear regression problem, suppose that = 12.48 and = 124.8. Then the percentage of variation explained must be 0.90.

Q: In a simple regression with a single explanatory variable, the multiple R is the same as the standard correlation between the Y variable and the explanatory X variable.

Q: The multiple R for a regression is the correlation between the observed Y values and the fitted Y values.

Q: The percentage of variation explained is the square of the correlation between the observed Y values and the fitted Y values.

Q: In a simple linear regression problem, if the percentage of variation explained is 0.95, this means that 95% of the variation in the explanatory variable X can be explained by regression.

Q: In a simple regression analysis, if the standard error of estimate = 15 and the number of observations n = 10, then the sum of the residuals squared must be 120.

Q: The regression line = 3 + 2X has been fitted to the data points (4, 14), (2, 7), and (1, 4). The sum of the residuals squared will be 8.0.

Q: In simple linear regression, the divisor of the standard error of estimate is n " 1; simply because there is only one explanatory variable of interest.

Q: In regression analysis, we can often use the standard error of estimate to judge which of several potential regression equations is the most useful.

Q: A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: = 32 + 8X. This implies that an increase of $1 in advertising is expected to result in an increase of $40 in sales.

Q: A regression analysis between weight (Y in pounds) and height (X in inches) resulted in the following least squares line: = 140 + 5X. This implies that if the height is increased by 1 inch, the weight is expected to increase on average by 5 pounds.

Q: A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: = 84 +7X. This implies that if there is no advertising, then the predicted amount of sales (in dollars) is $84,000.

Q: A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: = 84 +7X. This implies that if advertising is $800, then the predicted amount of sales (in dollars) is $140,000.

Q: In reference to the equation, , the value 0.10 is the expected change in Y per unit change in .

Q: A negative relationship between an explanatory variable X and a response variable Y means that as X increases, Y decreases, and vice versa.