Exam 13: 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 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.

A regression model was applied to a data set with 8 time-ordered observations.The residuals for these observations are given below. Calculate the Durbin-Watson statistic (d).

The standard error of the estimate (standard error)is the estimated standard deviation of the distribution of the independent variable (X)for all values of the dependent variable (Y).

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 SSE and SS(Total).

The simple coefficient of determination is the proportion of total variation explained by the regression line.

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 standard error.

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).Residuals are calculated for all of the randomly selected six months and ordered from smallest to largest.Determine the normal score for the third residual in the ordered array.

The ____________ assumption requires that all variation around the regression line should be equal at all possible values (levels)of the independent variable.

The _____________ is the range of the previously observed values of x.

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.

In simple regression analysis,the quantity is called the __________ sum of squares.

The correlation coefficient may assume any value between:

In simple regression analysis,the standard error is ___________ greater than the standard deviation of y values.

A data set with 7 observations yielded the following.Use the simple linear regression model. SSE = 1.117 Determine the 95 percent confidence interval for the average value of Y when x = 3.25.

The Durbin-Watson test statistic ranges from:

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 confidence interval for the average strength of a metal sheet when the average heating time is 2.5 minutes.

If r = -1,then we can conclude that there is a perfect relationship between X and Y.

In simple regression analysis,if the correlation coefficient is a positive value,then:

If there is significant autocorrelation present in a data set,the ________________ assumption is violated.

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