Exam 11: Correlation Coefficient and Simple Linear Regression Analysis

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. $\sum X$ = 30 $\sum X ^ { 2 }$ = 104 $\sum Y$ = 40 $\sum Y ^ { 2 }$ = 178 $\sum X Y$ = 134 -Calculate the 95% confidence interval for the slope.

Consider the following partial computer output from a simple linear regression analysis: Predictor Coef SE Coef Constant 5566.1 254.0 21.91 0.000 Independent Var -210.35 24.19 - S = _________ R-Sq = Analysis of Variance Source DF SS MS F P Regression 1 3963719 3963719 75.59 0.000 Residual Error 14 \_\_\_ 52439 Total 15 \_\_\_ -Calculate the SSE.

A local tire dealer wants to predict the number of tires sold each month.The dealer believes that the number of tires sold is a linear function of the amount of money invested in advertising.The dealer 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 $\hat { y }$ = 3 + 1x. $\sum X$ = 24 $\sum X ^ { 2 }$ = 124 $\sum Y$ = 42 $\sum Y ^ { 2 }$ = 338 $\sum X Y$ = 196 MSE = 4 -Using the sums of the squares given above,determine the 90% prediction interval for an individual month's tire sales when the advertising expenditure is $5000.

An experiment was performed on a certain metal to determine if the strength,in g/cm²,was a function of heating time,in minutes.The least-squares regression line was found to be $\hat { y }$ = 1 + 1x.What is the predicted value strength when the metal is heated for 4 minutes?

Determine the 95% confidence interval for the mean value of y when x = 9.00.Given: ? x = 129.03 and ? x² = 1178.547

One of the metal sheets used in the experiment was heated for 4 minutes had an observed strength of 6 g per square cm.Calculate the value of the residual for this observation.

Determine the 95% confidence interval for the mean value of y when x = 8.5. Givens: ∑ x = 163.65 and ∑ x² = 1763.418

The _____ distribution is used for testing the significance of the slope term.

Consider the following partial computer output from a simple linear regression analysis: Predictor Coef SE Coef Constant 5566.1 254.0 21.91 0.000 Independent Var -210.35 24.19 - S = _________ R-Sq = Analysis of Variance Source DF SS MS F P Regression 1 3963719 3963719 75.59 0.000 Residual Error 14 \_\_\_ 52439 Total 15 \_\_\_ -Write the equation of the least squares line.

The least-squares regression line is the line that minimizes: