Exam 11: Basic Regression Analysis

Suppose a rental car company uses simple linear regression to develop an equation that predicts the repair costs for each of its vehicles based on the mileage of the car (total miles driven).The company uses the following data on repair costs and miles driven for five of its cars: The intercept of the least squares regression line is:

Karina Burkholtz believes there is a linear connection between the hourly rate (x) that her company charges for its truck rentals and the number of weekly rental hours (y) that the company sells.The following data are available: The slope term (b) in the estimated regression equation is -8.The intercept term (a) is 237.Construct a 95% confidence interval estimate of E(y₁₂), the expected weekly rental hours for an hourly rate of $12.Report the upper bound for the interval.

The following data are available for a simple linear regression analysis attempting to link hours of training (x) to hourly output (y). In applying the least squares criterion, the slope (b) and the intercept (a) for the best-fitting line are b = 2.4 and a = 3.6.Compute the value of r, the correlation coefficient here.

In a simple linear regression analysis attempting to link lottery sales (y) to jackpot amount (x), the following data are available: The slope term (b) of the estimated regression equation turns out to be 3.5.The intercept term (a) turns out to be 20.Show the 95% prediction interval for sales for an individual case in which the jackpot is $9 (million).Show the upper bound for the interval.

The following data have been collected for a simple linear regression analysis relating sales (y) to price (x): In applying the least squares criterion, the slope (b) and the intercept (a) for the best-fitting line are b = -12 and a = 162.Produce the 99% confidence interval estimate of the population slope, β.Report the upper bound for your interval.

Partial regression results from a sample of 12 observations are shown below.Can we use the sample results shown here to reject a β = 0 null hypothesis at the 5% significance level?

The following data are available for a simple linear regression analysis attempting to link hours of training (x) to hourly output (y). The slope term in the estimated regression equation was 2.4.The intercept term (a) was 3.6.Show the 90% prediction interval for hourly output for an individual with 2.5 hours of training.Report the upper bound for the interval.

The manager of a local shopping mall uses simple linear regression to develop an equation that predicts the number of daily shoplifting incidents at the mall's stores based on the number of security guards employed.Below is a partial table showing the data that was used. The slope of the regression line is b = -1.2; the intercept of the regression line is a = 14.5. Calculate the residual associated with the last observation in the data set, where x = 9 and y = 3.

Needing a simple cost estimator for commercial construction costs in the city, you hope to find a useful linear relationship between cost (y) and floor space (x).You have data from a sample of four recently completed building projects: The estimated regression equation turns out to be y = 24 + 1.6x and s_y.x = 17.9.You want to construct an appropriate hypothesis test to determine whether we can use the sample data here to reject a β = 0 null hypothesis.Calculate the value of the proper test statistic, t_stat, for the test.

In regression analysis, which of the following is NOT a required assumption about the error term, $\varepsilon$ ?

Kareem Martin is trying to identify a linear relationship linking the amount of heat (x) applied in the final hardening stage to the heavy duty steel bolts that his company produces for bridge construction and the strength of those bolts (y).Below is a table showing data for a sample of five of the bolts. The slope for the least squares line is .22.The intercept is 320.Compute the "unexplained variation" (SSE) here.

Economist Joshua Grant is using linear regression to try to establish a link between the unemployment rate (x) and monthly home sales in the region (y).The following data are available: The slope term (b) in the estimated regression equation turns out to be -8.The intercept term (a) is 237.Explained variation (SSR) here would be _______.

Suppose you have done a simple linear regression analysis using a sample of 50 data points in an attempt to find a linear connection between worker overtime hours (x) and worker productivity (y) for employees of Sky Marketing Enterprises.The correlation coefficient turned out to be -.80. If total variation in y was 22500, then the standard error of estimate, s_y.x, must be ______.

Partial results from a regression analysis based on five observations are given below.Determine the standard error (standard deviation) of the sampling distribution of the estimated slope, b.

In simple linear regression, the least squares line fit to a sample of data will maximize the number of data points that will fall along that line.

Suppose a rental car company uses simple linear regression to develop an equation that predicts the repair costs for each of its vehicles based on the mileage of the car (total miles driven).The company uses the following data on repair costs and miles driven for five of its cars: The slope of the least squares regression line is:

In simple linear regression, the r² value measures the percentage of total variation in the sample data that cannot be explained by the x-to-y relationship that has been identified.

In residual analysis, if the assumptions about the error term are valid then the plot of the residuals against the corresponding x values should have a funnel shape.

The manager of a local shopping mall uses simple linear regression to develop an equation that predicts the number of daily shoplifting incidents at the mall's stores based on the number of security guards employed.The manager uses the following data: The slope of the regression line is b = -1.2; the intercept of the regression line is a = 14.5.Produce the 95% confidence interval for the estimate of the intercept of the population regression line and use it to complete the following sentence: With 95% confidence, the intercept of the population regression line is between ______ and ______.

In simple linear regression, the r² value is the ratio of SSE/SST.