Exam 14: Simple Linear Regression Analysis

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 ŷ = 3 + 1x. ∑X = 24 ∑X² = 124 ∑Y = 42 ∑Y² = 338 ∑XY = 196 MSE = 4 Using the sums of the squares given above, determine the 95 percent confidence interval for the slope.

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 ŷ = 1 + 1X. The time is in minutes, the strength is measured in pounds per square inch, MSE = .5, Σx = 30, and Σx² = 104. Determine the 95 percent prediction interval for the strength of a metal sheet when the average heating time is 2.5 minutes.

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. ∑X = 30 ∑X² = 104 ∑Y = 40 ∑Y² = 178 ∑XY = 134 Determine SSE and SS(Total).

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).

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 ŷ = 1 + 1X. Time is in minutes, strength is measured in pounds per square inch, MSE Σx = .5, Σx = 30, and Σx² = 104. The distance value has been found to be equal to .17143. Determine the 95 percent prediction interval for the strength of a metal sheet when the average heating time is 4 minutes.

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. ∑X = 30 ∑X² = 104 ∑Y = 40 ∑Y² = 178 ∑XY = 134 Find the t statistic and test H₀: b₁ ≤ 0 vs, H_a: b₁ > 0 at α = .05.

Any value of the error term in a regression model ________ any other value of the error term.

In simple regression analysis, if the correlation coefficient is a positive value, then

The point estimate of the variance in a regression model is

A data set with 7 observations yielded the following. Use the simple linear regression model. ∑X = 21.57 ∑X² = 68.31 ∑Y = 188.9 ∑Y² = 5,140.23 ∑XY = 590.83 SSE = 1.117 Calculate the coefficient of determination.

Consider the following partial computer output from a simple linear regression analysis. S = .4862R-Sq = ________ Analysis of Variance Calculate the t statistic used to test H₀: β₁ = 0 versus H_a: β₁ ≠ 0 at α = .001.

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. ∑X = 24 ∑X² = 124 ∑Y = 42 ∑Y² = 338 ∑XY = 196 Calculate the coefficient of determination.

A data set with 7 observations yielded the following. Use the simple linear regression model. ∑X = 21.57 ∑X² = 68.31 ∑Y = 188.9 ∑Y² = 5,140.23 ∑XY = 590.83 SSE = 1.117 Find the rejection point for the t statistic (α = .05). Test H₀: β₁ ≤ 0 vs. H_a: β₁ > 0.

If the Durbin-Watson statistic is greater than (4 − d_L), then we conclude that

In simple linear regression analysis, we assume that the variance of the independent variable (X) is equal to the variance of the dependent variable (Y).

Consider the following partial computer output from a simple linear regression analysis. S = .4862R-Sq = ________ Analysis of Variance Determine the 95 percent prediction interval for the mean value of y when x = 9.00. Givens: ∑x = 129.03, ∑x² = 1178.547

The coefficient of determination measures the ________ explained by the simple linear regression model.

The standard error of the estimate (standard error) is the estimated standard deviation of the distribution of the independent variable (X) for all values of the dependent variable (Y).

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?

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 ŷ = 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 β₁ = 0?