Exam 11: Correlation Coefficient and Simple Linear Regression Analysis

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

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 model yielded the following results. $\sum X$ = 24 $\sum X ^ { 2 }$ = 124 $\sum Y$ = 42 $\sum Y ^ { 2 }$ = 338 $\sum X Y$ = 196 -Find the rejection point for the t statistic at a = .05 and test H₀: ?₁= 0 vs.H_a: b₁¹ 0.

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 monthly tire sales (in thousands of tires)and monthly advertising expenditures (in thousands of dollars).The simple linear regression equation is $\hat { y }$ = 3 + 1x and 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:r = 0 vs.H_A:r ¹ 0 at a = .05. Failed to reject H₀,and there is no significant correlation.

The slope in the simple linear regression model represents the average change in the value of the dependent variable per unit change in the independent variable.

The _____ measures the strength and direction of the linear relationship between the dependent and the independent variable.

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 model yielded the following results. $\sum X$ = 24 $\sum X ^ { 2 }$ = 124 $\sum Y$ = 42 $\sum Y ^ { 2 }$ = 338 $\sum X Y$ = 196 -Complete the ANOVA table and determine the value of the F statistic.

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 -Find the t statistic and test H₀:

The coefficient of determination measures the proportion of observed variation in the _______ explained by the simple linear regression model.

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).The equation of the least squares line is, $\hat { Y }$ = 3 + 1x. -Provide an interpretation of the estimated slope.

A significant positive correlation between x and y implies that changes in x causes y to change.

Consider the following partial computer output from a simple linear regression analysis. Variable Coefficient Std. Deviation Intercept -28.13 -.088 .9309 1.12 .04891 22.895 .0001 .9722 -What is the estimated slope?

A simple linear regression on a data set of 12 ordered pairs (x,y)gave the following results: $\hat { y } = 54.23 + 1.45 x$ MSE = 1.1816 SS_xx = 0.9814 $\bar { x } = 10.8$ Compute a 95% confidence interval for the mean value of y when x = 8?

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 -Find the estimated y intercept and slope and write the equation of the least squares regression line.

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).The equation of the least squares line is, $\hat { Y }$ = 3 + 1x. -Provide an interpretation of the estimated y-intercept.

In a simple linear regression model,the y-intercept term is the mean value of y when x equals _____.

In simple regression analysis,r²measures the proportion of the variation in the dependent variable explained by the simple linear regression model.

What is the predicted value of y when x = 1,000?

What is the correlation coefficient?

A simple linear regression model is an equation that describes the straight-line relationship between a dependent variable and an independent variable.

Consider the following partial computer output from a simple linear regression analysis. Variable Coefficient Std. Deviation Intercept -28.13 -.088 .9309 1.12 .04891 22.895 .0001 .9722 -What is the predicted value of y when x = 1,000?