Q&A Hero

Q: When using regression analysis for descriptive purposes, which of the following is of importance? A) The size of the regression slope coefficient B) The sign of the regression slope coefficient C) The standard error of the regression slope coefficient D) All of the above

Q: Given the data below, one ran the simple regression analysis of Y on X. Y X 4 2 3 1 4 4 6 3 8 5 The relationship between Y and X is A) significant at the alpha = 1 percent level. B) significant at the alpha = 5 percent level. C) significant at the alpha = 10 percent level. D) not significant at the alpha = 10 percent level.

Q: A regression analysis between sales (Y) and advertising (X) (both in dollars) resulted in the following equation: = 100 + 2000X The above equation implies that an A) increase of $1 in advertising is correlated with an increase of $2,000 in sales. B) increase of $1 in advertising is correlated with an increase of $2 in sales. C) increase of $1 in advertising is correlated with an increase of $100 in sales. D) increase of $1 in advertising is correlated with an increase of $2100 in sales.

Q: Which of the following statements is true in simple linear regression? A) The standard error of the estimate is equal to the standard error of the slope. B) The total degrees of freedom are (n-2). C) The coefficient of determination is equal to the correlation of x and y. D) The p-value of the F test will equal the p-value of the t-test of the slope.

Q: Consider the following partially completed computer printout for a regression analysis where the dependent variable is the price of a personal computer and the independent variable is the size of the hard drive. Based on the information provided, which of the following statements is true if alpha = .05? A) The slope is not significantly different from 0 because p-value = 0.84 is greater than 0.05 B) The slope is significantly different from 0 because p-value = 9.95 is greater than 0.05 C) The slope is not significantly different from 0 because p-value = 9.95 is greater than 0.05 D) The slope is significantly different from 0 because p-value = 9.95En - 10 is less than 0.05

Q: Consider the following partially completed computer printout for a regression analysis where the dependent variable is the price of a personal computer and the independent variable is the size of the hard drive. Based on the information provided, what is the F statistic? A) About 8 .33 B) Just over 2.35 C) About 4.76 D) About 69.5

Q: Consider the following partially completed computer printout for a regression analysis where the dependent variable is the price of a personal computer and the independent variable is the size of the hard drive. Based on the information provided, what is the estimate for the standard error of the estimate for the regression model? A) Approximately 690.50 B) About 4,026 C) Just under 376.23 D) 476,800

Q: Consider the following partially completed computer printout for a regression analysis where the dependent variable is the price of a personal computer and the independent variable is the size of the hard drive. Based on the information provided, what percentage of the variation in the price of the personal computers is accounted for by the regression model using hard drive capacity as the independent variable? A) About 82 percent B) About 67 percent C) 217.75 D) About 66 percent

Q: Assuming that a regression has been conducted for a group of small companies where x = the number of employees at the company, y = annual revenue of the company (recorded in thousands of dollars), and the largest company included in the study had 82 employees. The resulting regression equation is = 59.2 + 83.4x. Which of the following is true? A) For each additional employee, revenue on average will increase by $83.4 B) A company with 2100 employees could be predicted to have average revenue of about $175 million. C) For each additional employee, revenue on average will increase by $59.2 thousand. D) This model should not be used to make predictions for companies with more than 82 employees.

Q: A recent study by a major financial investment company was interested in determining whether the annual percentage change in stock price for companies is linearly related to the annual percent change in profits for the company. The following data was determined for 7 randomly selected companies: % Change Stock Price % Change in Profit 8.4 4.2 9.5 5.6 13.6 11.2 -3.2 4.5 7 12.2 18.4 12 -2.1 -13.4 Based upon this sample information, which of the following is the regression equation? A) = 4.19 + .61x B) = 15.04 + 4.25x C) = 1.19 - 3.00x D) = 20.19 + .005x

Q: A recent study by a major financial investment company was interested in determining whether the annual percentage change in stock price for companies is linearly related to the annual percent change in profits for the company. The following data was determined for 7 randomly selected companies: % Change Stock Price % Change in Profit 8.4 4.2 9.5 5.6 13.6 11.2 -3.2 4.5 7 12.2 18.4 12 -2.1 -13.4 Based upon this sample information, what portion of variation in stock price percentage change is explained by the percent change in yearly profit? A) Approximately 70 percent B) Nearly 19 percent C) About 49 percent D) None of the above

Q: In a regression analysis situation, the standard error of the slope is: A) a measure of the variation in the regression slope from sample to sample. B) equal to the square root of the standard error of the estimate. C) a measure of the amount of change in y that will occur for a one-unit change in x. D) All of the above

Q: Which of the following statements is true with respect to a simple linear regression model? A) The regression slope coefficient is the square of the correlation coefficient. B) The percentage of variation in the dependent variable that is explained by the independent variable can be determined by squaring the correlation coefficient. C) It is possible that the correlation between a y and x variable might be statistically significant, but the regression slope coefficient could be determined to be zero since they measure different things. D) The standard error of the estimate is equal to the standard error of the slope.

Q: The following regression output is available. Notice that some of the values are missing. Given this information, what is the standard error of the estimate for the regression model? A) About 36.18 B) Approximately 6.02 C) About 1.98 D) 3.91

Q: The following regression output is available. Notice that some of the values are missing. Given this information, what is the test statistic for testing whether the regression slope coefficient is equal to zero? A) Approximately t = 3.04 B) About t = 2.19 C) About t = 9.24 D) About t = 2.39

Q: The following regression output is available. Notice that some of the values are missing. Given this information, what was the sample size used in the study? A) 8 B) 18 C) 9 D) 16

Q: The following regression output is available. Notice that some of the values are missing. Given this information, what percent of the variation in the y variable is explained by the independent variable? A) About 75 percent B) Approximately 57 percent C) Can't be determined without having the actual data available. D) About 25 percent

Q: Use the following regression results to answer the question below. In conducting a hypothesis test of the slope using a 0.05 level of significance, which of the following is correct? A) The slope differs significantly from 0 because p-value = 0.205 is greater than 0.05 B) The slope does not differ significantly from 0 because p-value = 0.205 is greater than 0.05 C) The slope differs significantly from 0 because p-value = 0.003 is less than 0.05 D) The slope does not differ significantly from 0 because p-value = 0.003 is less than 0.05

Q: Use the following regression results to answer the question below. How many observations were involved in this regression? A) 7 B) 8 C) 9 D) 10

Q: Use the following regression results to answer the question below. Which of the following is true? A) x explains about 88.5 percent of the variation in y. B) y explains about 88.5 percent of the variation in x. C) x explains about 78.4 percent of the variation in y. D) y explains about 78.4 percent of the variation in x.

Q: Use the following regression results to answer the question below. Which of the following is true? A) The correlation between x and y must be approximately 0.8851. B) The correlation between x and y must be approximately -0.8851. C) The correlation between x and y must be approximately 0.7835. D) The correlation between x and y must be approximately -0.7835.

Q: Which of the following statements is true with respect to a simple linear regression model? A) The percent of variation in the dependent variable that is explained by the regression model is equal to the square of the correlation coefficient between the x and y variables. B) If the correlation coefficient between the x and y variables is negative, the sign on the regression slope coefficient will also be negative. C) If the correlation between the dependent and the independent variable is determined to be significant, the regression model for y given x will also be significant. D) All of the above are true.

Q: Which of the following is NOT an assumption for the simple linear regression model? A) The individual error terms are statistically independent. B) The distribution of the error terms will be skewed left or right depending on the shape of the dependent variable. C) The error terms have equal variances for all values of the independent variable. D) The mean of the dependent variable value for all levels of x can be connected by a straight line.

Q: A study was done in which the high daily temperature and the number of traffic accidents within the city were recorded. These sample data are shown as follows: High Temperature Traffic Accidents 91 7 56 4 75 9 68 11 50 3 39 5 98 8 Given this data the sample correlation is: A) -0.57 B) 0.64 C) 1.54 D) 0.57

Q: A recent study of 15 shoppers showed that the correlation between the time spent in the store and the dollars spent was 0.235. Using a significance level equal to 0.05, which of the following is true? A) The null hypothesis that the population mean is equal to zero should be rejected and we should conclude that the true correlation is not equal to zero. B) Based on the sample data there is not enough evidence to conclude that the true correlation is different from zero. C) The sample correlation coefficient could be zero since the test statistic does not fall in the rejection region. D) The null hypothesis should be rejected because the test statistic exceeds the critical value.

Q: A recent study of 15 shoppers showed that the correlation between the time spent in the store and the dollars spent was 0.235. Using a significance level equal to 0.05, which of the following is the test statistic for testing whether the true population correlation is equal to zero? A) t = 0.245 B) t = 1.76 C) t = 2.1604 D) t = 0.872

Q: A recent study of 15 shoppers showed that the correlation between the time spent in the store and the dollars spent was 0.235. Using a significance level equal to 0.05, which of the following is the appropriate null hypothesis to test whether the population correlation is zero?

Q: The term that is given when two variables are correlated but there is no apparent connection between them is: A) spontaneous correlation. B) random correlation. C) spurious correlation. D) linear correlation.

Q: Assume that a medical research study found a correlation of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer. This could be interpreted to mean: A) the more vitamin A consumed, the lower a person's chances are of getting this type of cancer. B) the less vitamin A consumed, the lower a person's chances are of getting this type of cancer. C) the more vitamin A consumed, the higher a person's chances are of getting this type of cancer. D) vitamin A causes this type of cancer.

Q: Recently, an automobile insurance company performed a study of a random sample of 15 of its customers to determine if there is a positive relationship between the number of miles driven and the age of the driver. The sample correlation coefficient is r = .38. Given this information, and assuming that the test is to be performed at the .05 level of significance, which of the following is the correct test statistic? A) t = 1.4812 B) t = 1.7709 C) z = 2.114 D) t = 1.74

Q: Recently, an automobile insurance company performed a study of a random sample of 15 of its customers to determine if there is a positive relationship between the number of miles driven and the age of the driver. The sample correlation coefficient is r = .38. Given this information, which of the following is appropriate critical value for testing the null hypothesis at an alpha = .05 level? A) t = 2.6104 B) t = 1.7613 C) t = 1.7531 D) t = 1.7709

Q: Which of the following statements is correct? A) A scatter plot showing two variables with a positive linear relationship will have all points on a straight line. B) The stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.0. C) Two variables that are uncorrelated with one another may still be related in a nonlinear manner. D) All of the above are correct.

Q: If a sample of n = 30 people is selected and the sample correlation between two variables is r = 0.468, what is the test statistic value for testing whether the true population correlation coefficient is equal to zero? A) About t = 2.80 B) About t = -.3.01 C) t = 2.0484 D) Can't be determined without knowing the level of significance for the test.

Q: If a pair of variables have a strong curvilinear relationship, which of the following is true? A) The correlation coefficient will be able to indicate that curvature is present. B) A scatter plot will not be needed to indicate that curvature is present. C) The correlation coefficient will not be able to indicate the relationship is curved. D) The correlation coefficient will be equal to zero.

Q: If the population correlation between two variables is determined to be -0.70, which of the following is known to be true? A) There is a positive linear relationship between the two variables. B) There is a fairly strong negative linear relationship between the two variables. C) An increase in one of the variables will cause the other variable to decline by 70 percent. D) The scatter diagram for the two variables will be upward sloping from left to right.

Q: In analyzing the relationship between two variables, a scatter plot can be used to detect which of the following? A) A positive linear relationship B) A curvilinear relationship C) A negative linear relationship D) All of the above

Q: A high coefficient of determination (R2) implies that the regression model will be a good predictor for future values of the dependent variable given the value of the independent variable.

Q: A regression model that is deemed to have a regression slope coefficient that could be equal to zero should not be used for prediction since there is no established linear relationship between the x and y variable.

Q: Given the following regression equation, the predicted value for y when x = 0.5 is about 4.57

Q: A manufacturing company is interested in predicting the number of defects that will be produced each hour on the assembly line. The managers believe that there is a relationship between the defect rate and the production rate per hour. The managers believe that they can use production rate to predict the number of defects. The following data were collected for 10 randomly selected hours. Defects Production Rate Per Hour 20 400 30 450 10 350 20 375 30 400 25 400 30 450 20 300 10 300 40 300 Given these sample data, the simple linear regression model for predicting the number of defects is approximately = 5.67 + 0.048x.

Q: The prediction interval developed from a simple linear regression model will be at its narrowest point when the value of x used to predict y is equal to the mean value of x.

Q: When the intercept in a regression equation is deemed not significantly different from 0, then in making predictions for y, 0.0 should be used as the value of the intercept rather than the estimated intercept value.

Q: If the R-squared value for a regression model is high, the regression model will necessarily provide accurate forecasts of the y variable.

Q: When calculating prediction intervals for predicted values of y based on a given x, all 95 percent prediction intervals will be of equal width.

Q: When regression analysis is used for descriptive purposes, two of the main items of interest are whether the sign on the regression slope coefficient is positive or negative and whether the regression slope coefficient is significantly different from zero.

Q: A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected and the following regression results were observed: SUMMARY OUTPUT Given this output, the upper limit for the 95 percent confidence interval estimate for the true regression slope coefficient is approximately 0.28.

Q: A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected and the following regression results were observed: SUMMARY OUTPUT Given this output, the point estimate for the average tip per dollar amount of the bill is approximately $0.21.

Q: A positive population slope of 12 (1 = 12) means that a 1-unit increase in x causes an average 12-unit increase in y.

Q: In simple linear regression, the t-test for the slope and the F-test are both conducting the same hypothesis test.

Q: In a simple linear regression analysis, if the test statistic for testing the significance of the regression slope coefficient is 3.6, the F ratio from the analysis of variance table is known to be 12.96

Q: If the R-square value for a simple linear regression model is .80, the correlation between the two variables is known to be .64.

Q: The values of the regression coefficients are found such the sum of the residuals is minimized.

Q: If a simple least squares regression model is developed based on a sample where the two variables are known to be positively correlated, the sum of the residuals will be positive.

Q: If a simple least squares regression model is developed based on a sample where the two variables are known to be positively correlated, the sign on the regression coefficient will be positive also.

Q: State University recently randomly sampled seven students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: GPA HOURS 3.14 25 2.75 30 3.68 11 3.22 18 2.45 22 2.80 40 3.00 15 2.23 29 3.14 10 2.90 0 In testing the significance of the regression slope coefficient for the independent variable, HOURS, the calculated test statistic is approximately t = -1.47.

Q: State University recently randomly sampled seven students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: GPA HOURS 3.14 25 2.75 30 3.68 11 3.22 18 2.45 22 2.80 40 3.00 15 2.23 29 3.14 10 2.90 0 A regression model with HOURS as the independent variable has an R-square equal to approximately .46.

Q: Assume that we have found a regression equation of = 3.6 - 2.4x, and that the coefficient of determination is 0.72, then the correlation of x and y must be about 0.849.

Q: In a simple regression model, if the regression model is deemed to be statistically significant, it means that the regression slope coefficient is significantly greater than zero.

Q: If the correlation between the dependent variable and the independent variable is negative, the standard error of the regression slope coefficient in a simple linear regression model will also be negative.

Q: If the correlation of x and y is -0.65, then coefficient of determination is -0.4225.

Q: The standard error of the estimate for a simple linear regression model measures the variation in the slope coefficient from sample to sample.

Q: A study was recently done in which the following regression output was generated using Excel. SUMMARY OUTPUT Given this output, we would reject the null hypothesis that the population regression slope coefficient is equal to zero at the alpha = 0.05 level.

Q: A study was recently done in which the following regression output was generated using Excel. SUMMARY OUTPUT Given this, we know that approximately 57 percent of the variation in the y variable is explained by the x variable.

Q: If the sample value of the intercept turns out to be an illogical value, this is acceptable as long as x = 0 is not within the range of the data.

Q: The sum of the residuals in a least squares regression model will be zero only when the correlation between the x and y variables is statistically significant.

Q: If it is known that a simple linear regression model explains 56 percent of the variation in the dependent variable and that the slope on the regression equation is negative, then we also know that the correlation between x and y is approximately -0.75.

Q: You are given the following sample data for two variables: Y X 10 100 8 110 12 90 15 200 16 150 10 100 10 80 8 90 12 150 The regression model based on these sample data explains approximately 75 percent of the variation in the dependent variable.

Q: Given a sample of data for use in simple linear regression, the values for the slope and the intercept are chosen to minimize the sum of squared errors.

Q: In a study of 30 customers' utility bills in which the monthly bill was the dependent variable and the number of square feet in the house is the independent variable, the resulting regression model is = 23.40 + 0.4x. Based on this model, the expected utility bill for a customer with a home with 2,300 square feet is approximately $92.00.

Q: In a study of 30 customers' utility bills in which the monthly bill was the dependent variable and the number of square feet in the house is the independent variable, the resulting regression model is = 23.40 + 0.04x. Given this model, for a customer with a 2,000 square foot house and a monthly utility bill equal to $100.00, the residual from the regression model is approximately -$3.40.

Q: In a study of 30 customers' utility bills in which the monthly bill was the dependent variable and the number of square feet in the house is the independent variable, the resulting regression model is = 23.40 + 0.4x. Given this, the sample correlation coefficient is known to be positive.

Q: The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. The first observations in the sample for y and x were 300 and 18, respectively. Given this, the residual value for the first observation is approximately 81.6.

Q: Given a regression equation of = 16 + 2.3x we would expect that an increase in x of 2.0 would lead to an average increase of y of 4.6.

Q: The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. Given this model, the predicted value for y when x = 40 is 806.2.

Q: The sign on the intercept coefficient in a simple regression model will always be the same as the sign on the correlation coefficient.

Q: If the correlation between two variables is known to be statistically significant at the 0.05 level, then the regression slope coefficient will also be significant at the 0.05 level.

Q: If a set of data contains no values of x that are equal to zero, then the regression coefficient, b0, has no particular meaning.

Q: In developing a simple linear regression model it is assumed that the distribution of error terms will be normally distributed for all levels of x.

Q: In a simple regression model, the slope coefficient represents the average change in the independent variable for a one-unit change in the dependent variable.

Q: When a pair of variables has a positive correlation, the slope in the regression equation will always be positive.