Chapter 14: Linear Regression and Correlation Analysis

d. The correlation coefficient will not be able to indicate the relationship is curved.

If a pair of variables have a strong curvilinear relationship, which of the following is true? Select one: a. The correlation coefficient will be equal to zero. b. A scatter plot will not be needed to indicate that curvature is present. c. The correlation coefficient will be able to indicate that curvature is present. d. The correlation coefficient will not be able to indicate the relationship is curved.

d. The horizontal axis should show the fitted values for the dependent variable

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? Select one: a. The points should fall in a straight line. b. The plot should illustrate a bell-shaped distribution to show that the residuals are normally distributed. c. The plot should illustrate a cone shaped look. d. The horizontal axis should show the fitted values for the dependent variable.

b. a measure of the variation in the regression slope from sample to sample.

In a regression analysis situation, the standard error of the slope is: Select one: a. a measure of the amount of change in y that will occur for a one-unit change in x. b. a measure of the variation in the regression slope from sample to sample. c. equal to the square root of the standard error of the estimate. d. All of the above

d. All of the above

In analyzing the relationship between two variables, a scatter plot can be used to detect which of the following? Select one: a. A curvilinear relationship b. A negative linear relationship c. A positive linear relationship d. All of the above

d. Both A and B are true.

In analyzing the residuals to determine whether the simple regression analysis satisfies the regression assumptions, which of the following is true? Select one: a. The scatter plot of the residuals against the dependent variable should illustrate that the variation in residuals is the same over all levels of ^y. b. The histogram of the residuals should be approximately bell-shaped. c. Neither A nor B are true. d. Both A and B are true.

Coefficient of Determination

Indicates the goodness of fit of the regression equation to the data

Correlation Coefficient

Numerical quantity that measures the strength of the linear relationship between two variables (-1& 1)

Simple Linear Regression

Relationship between dependent variables and independent variables

Regression slope coefficient

The average change in the dependent variable for a unit change in the independent variable. May be positive or negative

Residual

The difference between the actual value of the dependent variable and the value predicted by the regression model

b. spurious correlation.

The term that is given when two variables are correlated but there is no apparent connection between them is: Select one: a. linear correlation. b. spurious correlation. c. random correlation. d. spontaneous correlation.

d. The average change in y of a one-unit change in x will be b1 units.

Which of the following is a correct interpretation for the regression slope coefficient? Select one: a. For each unit change in x, the dependent variable will change by b1 units. b. For a one-unit change in y, we can expect the value of the independent variable to change by b1 units on average. c. The average change in x of a one-unit change in y will be b1 units. d. The average change in y of a one-unit change in x will be b1 units.

c. Two variables that are uncorrelated with one another may still be related in a nonlinear manner.

Which of the following statements is correct? Select one: a. The stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.0. b. A scatter plot showing two variables with a positive linear relationship will have all points on a straight line. c. Two variables that are uncorrelated with one another may still be related in a nonlinear manner. d. All of the above are correct.

b. The p-value of the F test will equal the p-value of the t-test of the slope.

Which of the following statements is true in simple linear regression? Select one: a. The total degrees of freedom are (n-2). b. The p-value of the F test will equal the p-value of the t-test of the slope. c. The standard error of the estimate is equal to the standard error of the slope. d. The coefficient of determination is equal to the correlation of x and y.

d. All of the above are true.

Which of the following statements is true with respect to a simple linear regression model? Select one: a. If the correlation coefficient between the x and y variables is negative, the sign on the regression slope coefficient will also be negative. b. 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. 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.

b. The prediction interval generated from a simple linear regression model will be narrowest when the value of x used to generate the predicted y value is close to the mean value of x.

Which of the following statements is true? Select one: a. The prediction interval generated from a simple linear regression model will be widest when the value of x used to generate the predicted y value is close to the mean value of x. b. The prediction interval generated from a simple linear regression model will be narrowest when the value of x used to generate the predicted y value is close to the mean value of x. c. The higher the r-square value, the wider will be the prediction interval based on a simple linear regression model. d. The interval estimate for predicting a particular value of y given a specific x will be narrower than the interval estimate for the average value of y given a particular x.