Exam 13: Simple Linear Regression Analysis

Consider the following partial computer output from a simple linear regression analysis. S = 0.4862 R-Sq = ______ Analysis of Variance Determine the 95% confidence interval for the mean value of y when x = 9.00.Givens: $\Sigma$ x = 129.03 and $\Sigma$ x² = 1178.547

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 = 1 + 1X.The time is in minutes and the strength is measured in pounds per square inch. Determine the predicted value of y when x = 4.

Regression Analysis The local grocery store wants to predict the daily sales in dollars.The manager believes that the amount of newspaper advertising significantly affects the store sales.He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars)and advertising expenditures (in thousands of dollars).The Excel/Mega-Stat output given above summarizes the results of the regression model. In testing the population for significance at a significance level of .05,what is the rejection point condition for the two-sided test?

A simple regression analysis with 20 observations would yield ________ degrees of freedom error and _________ degrees of freedom total.

Regression Analysis The local grocery store wants to predict the daily sales in dollars.The manager believes that the amount of newspaper advertising significantly affects the store sales.He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars)and advertising expenditures (in thousands of dollars).The Excel/Mega-Stat output given above summarizes the results of the regression model. In testing the simple linear regression equation for significance at a significance level of .05,what is the rejection point condition?

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 = 3 + 1x. = 24 = 124 = 42 = 338 = 196 MSE = 4 Use the least squares regression equation and estimate the monthly tire sales when advertising expenditures is $4000.

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

Regression Analysis The local grocery store wants to predict the daily sales in dollars.The manager believes that the amount of newspaper advertising significantly affects the store sales.He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars)and advertising expenditures (in thousands of dollars).The Excel/Mega-Stat output given above summarizes the results of the regression model. What is the value of the simple coefficient of determination?

The following results were obtained from a simple regression analysis: = 37.2895 - (1.2024)X r²= .6744 s_b = .2934 ____________ is the proportion of the variation explained by the simple linear regression model.

Complete the following partial ANOVA table from a simple linear regression analysis with a sample size of 16 observations.Find the F test to test the significance of the model.

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 = 1 + 1X .The time is in minutes and the strength is measured in pounds per square inch,MSE = 0.5, = 30, = 104. Determine the 95% prediction interval for the strength of a metal sheet when the average heating time is 2.5 minutes.

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).The equation of the least squares line is, = 3 + 1x. Provide a managerial interpretation of the estimated slope.

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 monthly tire sales (in thousands of tires)and monthly advertising expenditures (in thousands of dollars).The simple linear regression equation is = 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: $\rho$ = 0 vs.H_A: $\rho$ $\neq$ 0 at $\alpha$ = .05.

Use the least squares regression equation, = 12.36 + 4.745(X),and determine the predicted value of Y when X = 3.25?

The experimental region is the range of the previously observed values of the dependent variable.

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

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 = 1 + 1X .The time is in minutes and the strength is measured in pounds per square inch,MSE = 0.5, = 30, = 104. Determine the 95% confidence interval for the mean value of metal strength when the average heating time is 4 minutes.

If one of the assumptions of the regression model is violated,performing data transformations on the ____________ can remedy the situation.

A ______________________ measures the strength of the relationship between a dependent variable (Y)and an independent variable (X).

A data set with 7 observations yielded the following.Use the simple linear regression model. = 21.57 = 68.31 = 188.9 = 5,140.23 = 590.83 SSE = 1.06 Calculate the coefficient of determination.