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Exam 14: Introduction to Linear Regression and Correlation Analysis

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Question 21

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Which of the following statements is true with respect to a simple linear regression model?

A) The percent of variation in the dependent variable that is explained by the regression model is equal to the square of the correlation coefficient between the x and y variables.
B) If the correlation coefficient between the x and y variables is negative, the sign on the regression slope coefficient will also be negative.
C) If the correlation between the dependent and the independent variable is determined to be significant, the regression model for y given x will also be significant.
D) All of the above are true.

E) B) and D)
F) C) and D)

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Question 22

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In a simple regression model, if the regression model is deemed to be statistically significant, it means that the regression slope coefficient is significantly greater than zero.

A) True
B) False

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Question 23

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If two variables are related in a positive linear manner, the scatter plot will show points on the x,y space that are generally moving from the lower left to the upper right.

If you were going to develop a scatter plot for the purpose of determining whether one of the assumptions of the regression model is being satisfied, which of the following is true?

When using regression analysis for descriptive purposes, which of the following is of importance?

A study was recently done in which the following regression output was generated using Excel. SUMMARY OUTPUT Given this, we know that approximately 57 percent of the variation in the y variable is explained by the x variable.

A perfect correlation between two variables will always produce a correlation coefficient of +1.0

When the correlation coefficient for the two variables was -0.23, it implies that the two variables are not correlated because the correlation coefficient cannot be negative.

The Public Utility Commission in a southern state is interested in describing the relationship between household monthly utility bills and the size of the house. A recent study of 30 randomly selected household resulted in the following regression results: Based on the information provided, indicate what, if any, conclusions can be reached about the relationship between utility bill and the size of the house in square feet.

The sum of the residuals in a least squares regression model will be zero only when the correlation between the x and y variables is statistically significant.

The difference between a scatter plot and a scatter diagram is that the scatter plot has the independent variable on the x-axis while the independent variable is on the Y-axis in a scatter diagram.

The following data for the dependent variable, y, and the independent variable, x, have been collected using simple random sampling: Compute the correlation coefficient.

Which of the following statements is true with respect to a simple linear regression model?

You are given the following sample data for two variables: The sample correlation coefficient for these data is approximately r = 0.755.

A recent study by a major financial investment company was interested in determining whether the annual percentage change in stock price for companies is linearly related to the annual percent change in profits for the company. The following data was determined for 7 randomly selected companies: Based upon this sample information, which of the following is the regression equation?

Which of the following statements is true?

The following regression output was generated based on a sample of utility customers. The dependent variable was the dollar amount of the monthly bill and the independent variable was the size of the house in square feet. Based on this regression output, what is the 95 percent confidence interval estimate for the population regression slope coefficient?

The term that is given when two variables are correlated but there is no apparent connection between them is:

A positive population slope of 12 (β1 = 12) means that a 1-unit increase in x causes an average 12-unit increase in y.

Consider the following partially completed computer printout for a regression analysis where the dependent variable is the price of a personal computer and the independent variable is the size of the hard drive. Based on the information provided, what is the estimate for the standard error of the estimate for the regression model?