Exam 13: Simple Linear Regression Analysis

Consider the following partial computer output from a simple linear regression analysis. Analysis of Variance Calculate the MSE.

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. Determine the values of SSE and SST.

In a simple linear regression model,the coefficient of determination not only indicates the strength of the relationship between the independent and dependent variables,but also shows whether the relationship is positive or negative.

Consider the following partial computer output from a simple linear regression analysis. Calculate the correlation coefficient.

Consider the following partial computer output from a simple linear regression analysis. Analysis of Variance What is the explained variance?

A data set with 7 observations yielded the following.Use the simple linear regression model. SSE = 1.117 Find the estimated slope.

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.The simple linear regression equation is The time is in minutes and the strength is measured in pounds per square inch.One of the 10 metal sheets was heated for 4 minutes and the resulting strength was 6 lbs.per square inch.Calculate the value of the residual for this observation.

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

When there is positive autocorrelation,over time,negative error terms are followed by positive error terms and positive error terms are followed by negative error terms.

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. Determine the value of the estimated y-intercept.

In simple regression analysis,r² is a percentage measure and measures the proportion of the variation explained by the simple linear regression model.

An experiment was performed on a certain metal to determine if the strength is a function of heating time.The 95 percent confidence interval for the average strength of a metal sheet when the average heating time is 4 minutes is from 4.325 to 5.675.Therefore,we are confident at α = .05 that the average strength of this metal heated for four minutes is between 4.325 and 5.675 pounds per square inch.Do you agree or disagree with this statement?

What value of the Durbin-Watson statistic indicates that there is no autocorrelation present in time-ordered data?

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. MSE = 4 Using the sums of the squares given above,determine the 90 percent confidence interval for the mean value of monthly tire sales when the advertising expenditure is $5000.

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

Consider the following partial computer output from a simple linear regression analysis. Analysis of Variance Test to determine if there is a significant correlation between x and y.Use H₀: ρ = 0 versus H_a: ρ ≠ 0 with α = .01.Show the test statistic used in the decision.

The following results were obtained as part of a simple regression analysis: The null hypothesis of no linear relationship between the dependent variable and the independent variable:

A data set with 7 observations yielded the following.Use the simple linear regression model. SSE = 1.117 Find the estimated y-intercept.

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. Find the rejection point for the t statistic at α = .05 and test H₀: β₁ = 0 vs.H_a: β₁ ≠ 0.

Based on 25 time-ordered observations from a simple regression model,we have determined the Durbin-Watson statistic,d = 1.39.At α = .05,test to determine if there is any evidence of positive autocorrelation.State your conclusions.