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Q:
The odds of an event occurring is the probability that the event will not occur divided by the probability that the event will occur.
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A studentized residual for an observation that is greater than 2 in absolute value is evidence that the observation is an outlier.
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Dfbetas and Dffits are statistics used to determine an outlier.
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Leverage value is a statistic used to determine an outlier.
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The critical value for Dfbetas statistics is 1.
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Cook's distance measure is used to detect if an outlier might influence the estimate of a model's parameter.
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It is appropriate to use an interaction variable if the relationship between the dependent variable and one of the independent variables depends on the value of theother independent variable.
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A partial F test is used to assess when at least one variable in a subset of squared and interaction variables in the multiple regression model is significant.
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Backward elimination regression is an automatic model-building procedure.
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Using squared and interaction variables in a multiple regression model results in extreme multicollinearity.
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If a particular multiple regression model has a small value of the C statistic and C for this model is less than k+1, where k is the number of independent variables in the model, then the model should be considered biased and therefore undesirable.
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In contrast to stepwise regression, backward elimination is an iterative model selection procedure that begins withall potential independent variables and then attempts to remove them one at a time based on the p-value of the independent variable.
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In a multiple regression mode, if the largest variance inflation factor (VIF) is 21.6, then it can be concluded that there are indications of multicollinearity.
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In comparing regression models, the regression model with the largest R2will also have the smallest standard error (s).
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Even when an unimportant variable is added to a regression model, the explained variation will increase.
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The variance inflation factor measures the relationship between the dependent variable and the rest of the independent variables in the regression model.
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When the quadratic regression model y = 0 + 1x + 2x2 + is used, the term 1shows the rate of curvature of the parabola.
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If we are predicting y when the values of the independent variables are x01, x02, . . . , x0k, the farther the values of x01, x02, . . . , x0kare from the center of the observed data, the smaller the distance value and the more precise the associated confidence and prediction intervals.
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In a multiple regression analysis, if the normal probability plot exhibits approximately a straight line, then it can be concluded that the assumption of normality is not violated.
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The assumption of independent error terms in regression analysis is often violated when using time-series data.
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The normal plot is a residual plot that checks the normality assumption.
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Testing the contribution of individual independent variables with ttests is performed prior to the Ftest for the model in multiple regression analysis.
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The multiple correlation coefficient can assume any value between zero and 1, inclusive.
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An application of the multiple regression model generated the following results involving the F test of the overall regression model:p-value= .0012, R2 = .67, and s = .076. Thus, the null hypothesis, which states that none of the independent variables are significantly related to the dependent variable, should be rejected at the .05 level of significance.
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For the same point estimate of the dependent variable and the same level of significance, the confidence interval is always wider than the corresponding prediction interval.
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When the F test is used to test the overall significance of a multiple regression model, if the null hypothesis is rejected, it can be concluded that all of the independent variables x1, x2, . . . ,xk are significantly related to the dependent variable y.
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Because multiple regression models consist of multiple independent variables, residual analysis cannot be performed.
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A ttest is used in testing the significance of an individual independent variable.
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In a regression model, a value of the error term depends upon other values of the error term.
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In a regression model, at any given combination of values of the independent variables, the population of potential error terms is assumed to have an F distribution.
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The error term in the regression model describes the effects of all factors other than the independent variables on y (response variable) .
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Regression models that employ more than one independent variable are referred to as multiple regression models.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of monthly tire sales (in thousands of tires) and monthly advertising expenditures (in thousands of dollars). Residuals are calculated for all of the randomly selected six months and ordered from smallest to largest. Determine the normal score for the smallest residual.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of monthly tire sales (in thousands of tires) and monthly advertising expenditures (in thousands of dollars). The simple linear regression equation is Å· = 3 + 1x. The dealer randomly selects one of the six observations, with a monthly sales value of 8,000 tires and monthly advertising expenditures of $7,000. Calculate the value of the residual for this observation.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of monthly tire sales (in thousands of tires) and monthly advertising expenditures (in thousands of dollars). The simple linear regression equation is Å· = 3 + 1x, and the sample correlation coefficient (r2) = .6364. Test to determine if there is a significant correlation between the monthly tire sales and monthly advertising expenditures. Use H0: = 0 vs. HA: 0 at = .05.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression equation of the least squares line is Å· = 3 + 1x.MSE = 4Using the sums of the squares given above, determine the 90 percent prediction interval for tire sales in a month when the advertising expenditure is $5,000.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression equation of the least squares line is Å· = 3 + 1x. MSE = 4
Using the sums of the squares given above, determine the 90 percent confidence interval for the mean value of monthly tire sales when the advertising expenditure is $5,000.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression equation of the least squares line is Å· = 3 + 1x.Using the sums of the squares given above, determine the 95 percent confidence interval for the slope.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression equation of the least squares line is Å· = 3 + 1x. MSE = 4
Use the least squares regression equation and estimate the monthly tire sales when advertising expenditures = $4,000.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results. Calculate the sample correlation coefficient.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results. Calculate the coefficient of determination.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results.Find the rejection point for the t statistic at = .05 and test H0: 1 = 0 vs. Ha: 1 0.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results.Find the rejection point for the t statistic at = .05 and test H0: 1 0 vs. Ha: 1 > 0.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results. Calculate the standard error.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results. Determine the value of the estimated y-intercept.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results. Find the estimated slope.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results. Determine the value of the F statistic.
Q:
A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results.Determine the values of SSE and SST.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. The sample size consists of 10 metal sheets. Residuals are calculated for all 10 metal sheets and ordered from smallest to largest. Determine the normal point for the second largest residual (ninth residual in the ordered array).
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. The sample size consists of 10 metal sheets. Residuals are calculated for all 10 sheets and ordered from smallest to largest. Determine the normal point for the smallest residual.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. The simple linear regression equation is = 1 + 1X, and the sample coefficient of determination (r2) = .7777. The time is in minutes and the strength is measured in pounds per square inch. Test to determine if there is a significant correlation between the heating time and strength of the metal. Using H0: = 0 vs. HA: 0 at = .05, determine the test statistic and decision.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. The 95 percent confidence interval for the average strength of a metal sheet when the average heating time is 4 minutes is from 4.325 to 5.675. Therefore, we are confident at = .05 that the average strength of this metal heated for four minutes is between 4.325 and 5.675 pounds per square inch. Do you agree or disagree with this statement?
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. The 95 percent prediction interval for the strength of a metal sheet when the average heating time is 4 minutes is from 3.235 to 6.765. We are 95 percent confident that an individual sheet of metal heated for four minutes will have strength of at least 4 pounds per square inch. Do you agree with this statement?
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Partial results based on a sample of 10 metal sheets are given below. The simple linear regression equation is = 1 + 1X. The time is in minutes, the strength is measured in pounds per square inch, MSE = 0.5, = 30, and = 104. Determine the 95 percent confidence interval for the average strength of a metal sheet when the average heating time is 2.5 minutes.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Partial results based on a sample of 10 metal sheets are given below. The simple linear regression equation is = 1 + 1X. The time is in minutes, the strength is measured in pounds per square inch, MSE = 0.5, = 30, and = 104. Determine the 95 percent prediction interval for the strength of a metal sheet when the average heating time is 2.5 minutes.
Q:
An experiment was performed on a certain metal to determine if its strength is a function of heating time. Partial results based on a sample of 10 metal sheets are given below. The simple linear regression equation is = 1 + 1X . Time is in minutes, strength is measured in pounds per square inch, MSE = 0.5, = 30, and = 104. The distance value has been found to be equal to 0.17143. Determine the 95 percent prediction interval for the strength of a metal sheet when the average heating time is 4 minutes.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Partial results based on a sample of 10 metal sheets are given below. The simple linear regression equation is = 1 + 1X. The time is in minutes, the strength is measured in pounds per square inch, MSE = 0.5, = 30, and = 104. Determine the 95 percent confidence interval for the mean value of metal strength when the average heating time is 4 minutes.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. The sample size consists of 10 metal sheets. The simple linear regression equation is = 1 + 1X. The time is in minutes and the strength is measured in pounds per square inch. One of the 10 metal sheets was heated for 4 minutes and the resulting strength was 6 lb per square inch. Calculate the value of the residual for this observation.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. The simple linear regression equation is = 1 + 1X. The time is in minutes and the strength is measured in pounds per square inch. The 95 percent confidence interval for the slope is from .564 to 1.436. Can we reject 1 = 0?
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model. Calculate the coefficient of determination.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model. Calculate the correlation coefficient.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model. Calculate the 95 percent confidence interval for the slope.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model. Find the t statistic and test H0: b1 ≤ 0 vs. Ha: b1 > 0 at α = .05.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model. Determine the standard error.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model. Determine the value of the F statistic.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model. Determine SSE and SS(Total).
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Using the simple linear regression model, find the estimated y-intercept and slope and write the equation of the least squares regression line.
Q:
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Using the simple linear regression model, find the estimated y-intercept.
Q:
Use the following results obtained from a simple linear regression analysis with 12 observations.= 37.2895 - (1.2024)Xr2 = .6744sb = .2934Test to determine if there is a significant negative relationship between the independent and dependent variables at = .05. Give the test statistic and the resulting conclusion.
Q:
Regression analysis.A local grocery store wants to predict its daily sales in dollars. The manager believes that the amount of newspaper advertising significantly affects sales. He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/MegaStat output given above summarizes the results of the regression model.Determine a 95 percent confidence interval estimate of the daily average store sales based on $3,000 advertising expenditures. The distance value for this particular prediction is reported as .164.
Q:
Regression analysis.A local grocery store wants to predict its daily sales in dollars. The manager believes that the amount of newspaper advertising significantly affects sales. He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/MegaStat output given above summarizes the results of the regression model.What are the limits of the 99 percent prediction interval of the daily sales in dollars of an individual grocery store that has spent $3,000 on advertising expenditures? The distance value for this particular prediction is reported as .164.
Q:
Regression AnalysisA local grocery store wants to predict its daily sales in dollars. The manager believes that the amount of newspaper advertising significantly affects sales. He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/MegaStat output given above summarizes the results of the regression model.If the manager decides to spend $3,000 on advertising, based on the simple linear regression results given above, what are the estimated sales?
Q:
Regression AnalysisA local grocery store wants to predict its daily sales in dollars. The manager believes that the amount of newspaper advertising significantly affects sales. He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/MegaStat output given above summarizes the results of the regression model.What are the limits of the 95 percent confidence interval for the population slope?
Q:
Regression Analysis A local grocery store wants to predict its daily sales in dollars. The manager believes that the amount of newspaper advertising significantly affects sales. He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/MegaStat output given above summarizes the results of the regression model.
What is the value of the simple coefficient of determination?
Q:
Regression Analysis A local grocery store wants to predict its daily sales in dollars. The manager believes that the amount of newspaper advertising significantly affects sales. He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/MegaStat output given above summarizes the results of the regression model.
At a significance level of .05, test the significance of the slope and state your conclusion.
Q:
Regression Analysis A local grocery store wants to predict its daily sales in dollars. The manager believes that the amount of newspaper advertising significantly affects sales. He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/MegaStat output given above summarizes the results of the regression model.
What is the estimated simple linear regression equation?
Q:
The following results were obtained from a simple regression analysis.Ŷ = 37.2895 - (1.2024)Xr2 = .6744sb = .2934What is the proportion of the variation explained by the simple linear regression model?
Q:
The following results were obtained from a simple regression analysis.Ŷ = 37.2895 - 1.2024Xr2 = .6744sb = .2934When X (independent variable) is equal to zero, what is the estimated value of Y (dependent variable)?
Q:
The following results were obtained from a simple regression analysis.Ŷ = 37.2895 - 1.2024Xr2 = .6744 sb = .2934For each unit change in X (independent variable), what is the estimated change in Y (dependent variable)?
Q:
A ______________________ measures the strength of the relationship between a dependent variable (Y) and an independent variable (X).
A. coefficient of determination
B. correlation coefficient
C. slope
D. standard error