Exam 13: Simple Linear Regression Analysis

The slope of the simple linear regression equation represents the average change in the value of the dependent variable per unit change in the independent variable (X).

In simple linear regression analysis,we assume that the variance of the independent variable (X)is equal to the variance of the dependent variable (Y).

A data set with 7 observations yielded the following.Use the simple linear regression model. SSE = 1.117 Find the rejection point for the t statistic (α = .05).Test H₀: β₁ ≤ 0 vs.H_a: β₁> 0.

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

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. Calculate the correlation coefficient.

Use the following results obtained from a simple linear regression analysis with 12 observations. Test to determine if there is a significant negative relationship between the independent and dependent variables at α = .05.Give the test statistic and the resulting conclusion.

Consider the following partial computer output from a simple linear regression analysis. Analysis of Variance What is the estimated y-intercept?

A data set with 7 observations yielded the following.Use the simple linear regression model. SSE = 1.117 Calculate the standard error.

Consider the following partial computer output from a simple linear regression analysis. Analysis of Variance What is the predicted value of y when x = 9.00?

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

After plotting the data points on a scatter diagram,we have observed an inverse relationship between the independent variable (X)and the dependent variable (Y).Therefore,we can expect both the sample ___________ and the sample _____________ to be negative values.

Consider the following partial computer output from a simple linear regression analysis. Test H₀: β₁ ≤ 0 vs.H_a: β₁> 0.

Consider the following partial computer output from a simple linear regression analysis. S = 0.4862 R-Sq = 0.7286 Analysis of Variance What is the correlation coefficient?

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

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 The time is in minutes,the strength is measured in pounds per square inch,MSE = 0.5, Determine the 95 percent prediction interval for the strength of a metal sheet when the average heating time is 4 minutes.The distance value has been found to be equal to 0.17143.

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

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

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

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. Calculate the coefficient of determination.

When using simple linear regression,we would like to use confidence intervals for the ___________ and prediction intervals for the ___________ at a given value of x.