TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, the normality of error assumption appears to have been violated.

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, what is the p-value for testing whether there is a linear relationship between revenue and the number of downloads at a 5% level of significance?

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to table 13-11, which of the following is the correct interpretation for the slope coefficient? A) For each increase of 1 download, the expected revenue is estimated to increase by $ 3.7297. B) For each increase of 1 thousand downloads, the expected revenue is estimated to increase by $ 3.7297 thousands. C) For each increase of 1 dollar in expected revenue, the expected number of downloads is estimated to increase by 3.7297. D) For each increase of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.

The slope coefficient represents the change in the predicted revenue for a one-unit increase in downloads. In this case, the predictor variable is measured in thousands, so the slope coefficient should also be interpreted in thousands. Therefore, the correct interpretation is: "For each increase of 1 thousand downloads, the expected revenue is estimated to increase by $3.7297 thousands."

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, what are, respectively, the lower and upper limits of the 95% confidence interval estimate for the average change in revenue as a result of a one thousand increase in the number of downloads?

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, which of the following assumptions appears to have been violated? A) normality of error B) homoscedasticity C) independence of errors D) None of the above.

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, what are, respectively, the lower and upper limits of the 95% confidence interval estimate for population slope?

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, what is the standard deviation around the regression line?

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, what is the critical value for testing whether there is a linear relationship between revenue and the number of downloads at a 5% level of significance?

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, what is the standard error of estimate?

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, there is sufficient evidence that revenue and the number of downloads are linearly related at a 5% level of significance.

The output from a simple linear regression indicates a significant relationship between revenue and the number of downloads, and the residual plot and normal probability plot suggest that the assumptions of linearity and normality are reasonable. Therefore, there is sufficient evidence to support the conclusion that revenue and the number of downloads are linearly related at a 5% level of significance.

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, predict the revenue when the number of downloads is 30 thousands.

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, the null hypothesis for testing whether there is a linear relationship between revenue and the number of downloads is "There is no linear relationship between revenue and the number of downloads."

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, what is the value of the test statistic for testing whether there is a linear relationship between revenue and the number of downloads?

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, the homoscedasticity of error assumption appears to have been violated.

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, the Durbin-Watson statistic is inappropriate for this data set.

The Durbin-Watson statistic is used to test for autocorrelation in the residuals of a regression model. However, in this case, we are looking at the residual plot and normal probability plot for the data set, which can also reveal the presence of autocorrelation. Therefore, the Durbin-Watson statistic is not necessary and may not be applicable.

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, which of the following is the correct null hypothesis for testing whether there is a linear relationship between revenue and the number of downloads? A) H 0 : b 1 = 0 B) H 0 : b 1 ≠ 0 C) H 0 : β 1 = 0 D) H 0 : β 1 ≠ 0

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, there appears to be autocorrelation in the residuals.

The answer of TABLE 13-11 A computer software developer would like...

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, the null hypothesis that there is no linear relationship between revenue and the number of downloads should be reject at a 5% level of significance.

This conclusion can be drawn from the regression output, where the p-value for the coefficient of the number of downloads is less than 0.05, indicating a statistically significant linear relationship. The residual plot and normal probability plot also suggest that the linear regression assumptions are met. Therefore, we reject the null hypothesis and conclude that there is a linear relationship between revenue and the number of downloads.

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, which of the following is the correct alternative hypothesis for testing whether there is a linear relationship between revenue and the number of downloads? A) H 1 : b 1 = 0 B) H 1 : b 1 ≠ 0 C) H 1 : β 1 = 0 D) H 1 : β 1 ≠ 0

The correct alternative hypothesis for testing whether there is a linear relationship between revenue and the number of downloads is H 1 : β 1 ≠ 0, which is choice D. This hypothesis states that there is a nonzero linear relationship between the two variables, which is what we typically want to test in a simple linear regression. Choices A and B have a typo, as b 1 should be β 1 . Choice C sets the alternative hypothesis equal to zero, which would imply no relationship between the variables.

TABLE 13-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 13-11, which of the following is the correct interpretation for the coefficient of determination? A) 74.67% of the variation in revenue can be explained by the variation in the number of downloads. B) 75.54% of the variation in revenue can be explained by the variation in the number of downloads. C) 74.67% of the variation in the number of downloads can be explained by the variation in revenue. D) 75.54% of the variation in the number of downloads can be explained by the variation in revenue.

The coefficient of determination (R-squared) is 0.7554, which means that 75.54% of the variation in revenue can be explained by the variation in the number of downloads. Option A is incorrect because it reverses the dependent and independent variables.

Quiz 13: Simple Linear Regression

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