Exam 13: Simple Linear Regression Analysis

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 and the sample coefficient of determination (r²)= .7777.The time is in minutes and the strength is measured in pounds per square inch.Test to determine if there is a significant correlation between the heating time and strength of the metal.Using H₀: ρ = 0 vs.H_A: ρ ≠ 0 at α = .05,determine the test statistic and decision.

In a simple linear regression model,the slope term is the change in the mean value of y associated with _____________ in x.

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. Find the t statistic and test H₀: b₁ ≤ 0 vs.H_a: b₁> 0 at α = .05.

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

The least squares point estimates of the simple linear regression model minimize the ____________.

The strength of the relationship between two quantitative variables can be measured by:

The following time-sequenced observations of actual and predicted values of the dependent variable (demand)are obtained from a simple regression model.Determine the Durbin-Watson statistic (d).

If successive values of the residuals are close together,then there is a ___________ autocorrelation,and the value of the Durbin-Watson statistic is _________.

The simple linear regression (least squares method)minimizes:

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 Use the least squares regression equation and estimate the monthly tire sales when advertising expenditures = $4000.

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 F statistic.

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

For a given data set,specific value of X,and confidence level,if all the other factors are constant,the confidence interval for the mean value of Y will ___________ be wider than the corresponding prediction interval for the individual value of Y.

The ___________ ther²,and the __________ thes (standard error),the stronger the relationship between the dependent variable and the independent variable.

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. 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.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 the strength is a function of heating time.The sample size consists of 10 metal sheets.Residuals are calculated for all 10 sheets and ordered from smallest to largest.Determine the normal point for the smallest residual.

The ____________________ is the proportion of the total variation in the dependent variable explained by the regression model.

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 ŷ = 3 + 1x,and the 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: ρ = 0 vs.H_A: ρ ≠ 0 at α = .05.

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. Using the simple linear regression model,find the estimated y-intercept.