Exam 14: Simple Linear Regression Analysis

The following results were obtained from a simple regression analysis: Ŷ = 37.2895 - 1.2024X r² = .6744 s_b = .2934 For each unit change in X (independent variable),what is the estimated change in Y (dependent variable)?

The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.

For the same set of observations on a specified dependent variable,two different independent variables were used to develop two separate simple linear regression models.A portion of the results is presented below. Model 1 Model 2 =.92 =.85 s=1.65s=1.91 Based on the results given above,we can conclude that:

The Durbin-Watson test statistic ranges from:

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.

The ___________ of the simple linear regression model is the value of y when the mean value of x is zero.

A multiple regression model was applied to a data set with 8 time ordered observations.The residuals for these observations are given below.

Which of the following is a violation of one of the major assumptions of the simple regression model?

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

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.

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.The dealer randomly selects one of the six observations,with a monthly sales value of 8000 tires and monthly advertising expenditures of $7000.Calculate the value of the residual for this observation.

The least squares simple linear regression line minimizes the sum of the vertical deviations between the line and the data points.

Which of the following is a violation of the independence assumption?

The simple linear regression (least squares method)minimizes:

Use the following results obtained from a simple linear regression analysis with 12 observations.

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.

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.

Consider the following partial computer output from a simple linear regression analysis with a sample size of 16 observations.Find the t test to test the significance of the model.

Use the least squares regression equation,

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.