Homework 9
If the coefficient of correlation is a positive value, then the regression equation a. must have a positive slope b. must have a negative slope c. could have either a positive or a negative slope d. must have a positive y-intercept
A
If the coefficient of determination is equal 0.8, then a. the percentage of variation in the dependent variable explained by the variation in the independent variable is 80% b. the percentage of variation in the dependent variable explained by the variation in the independent variable is 0.8% c. the percentage of variation in the independent variable explained by the variation in the dependent variable is 80% d. the percentage of variation in the independent variable explained by the variation in the dependent variable is 0.8%
A
In regression analysis, the variable that is being predicted is the a. dependent variable b. independent variable c. intervening variable d. is usually x
A
Correlation analysis is used to determine a. the equation of the regression line b. the strength of the relationship between the dependent and the independent variables c. a specific value of the dependent variable for a given value of the independent variable d. None of these alternatives is correct
B
In a regression analysis if R2 = 1, then a. SSE must also be equal to one b. SSE must be equal to zero c. SSE can be any positive value d. SSE must be negative
B
In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is a. 0.6667 b. 0.6000 c. 0.4000 d. 1.5000
B
In the estimated regression equation y^ = b0 + b1x the value of for a given value of x represents a. the estimate of the expected value of y b. the estimate of the expected value of y for a given x c. the estimate of the expected value of x d. the change in the dependent variable as the independent variable increases by 1 unit
B
The equation that describes how the dependent variable (y) is related to the independent variable (x) is called a. the correlation model b. the regression model c. estimated regression equation d. regression equation
B
When describing the equation that best fits the observations characterized by (x, y), the least squares method minimizes a. the sum of deviations of actual values y from the predicted values y ^ b. the sum of squares error c. the sum of absolute values of deviations of actual values y from the predicted values y^ d. the total sum of squares
B
Which of the following measures the variation in the dependent variable that is explained by variables other than the independent variable in simple regression analysis? a. standard error b. sum of squares error c. sum of squares regression d. total sum of squares
B
In the estimated regression equation y^ = b0 + b1x the value of represents a. predicted value of y given a value of x b. independent variable c. y-intercept of the straight line d. slope of the straight line
C
Larger values of R2 imply that the observations are more closely grouped about the a. average value of the independent variables b. average value of the dependent variable c. estimated regression line d. origin
C
Regression analysis is a statistical procedure for developing a mathematical equation that describes how a. one independent and one or more dependent variables are related b. several independent and several dependent variables are related c. one dependent and one or more independent variables are related d. None of these alternatives is correct
C
The model developed from sample data that has the form y^ = b0 + b1x is known as the a. regression equation b. correlation equation c. estimated regression equation d. regression model
C
Two variables have a correlation coefficient equal to +0.55 from a sample size of 8. Which one of the following statements describes the results of the hypothesis test that the population correlation coefficient is greater than zero using α = 0.05? The critical value of t-statistic associated with the significance level in this question is 1.94. a. Because the test statistic is greater than the critical value, we fail to reject the null hypothesis and conclude that the population correlation coefficient is not greater than zero. b. Because the test statistic is greater than the critical value, we can reject the null hypothesis and conclude that the population correlation coefficient is greater than zero. c. Because the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that the population correlation coefficient is not greater than zero. d. Because the test statistic is less than the critical value, we can reject the null hypothesis and conclude that the population correlation coefficient is not greater than zero.
C
Which distribution is used to test the significance of the population correlation coefficient? a. standard normal distribution b. Student's t distribution with df = n - 1 c. Student's t distribution with df = n - 2 d. F-distribution
C
Which of the following measures how consistent the slope of the regression equation would be if several sets of samples from the population were selected and the regression equations were derived for each of them? a. correlation coefficient b. coefficient of determination c. standard error of the slope d. standard error of the estimate
C
Which technique enables us to describe a straight line that best fits observations characterized by the pair of values (x, y)? a. analysis of variance b. correlation analysis c. simple regression analysis d. hypothesis testing
C
A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation y^ = 30,000 + 4x The above equation implies that an a. increase of $4 in advertising is associated with an average increase of $4,000 in sales b. increase of $1 in advertising is associated with an average increase of $4 in sales c. increase of $1 in advertising is associated with an average increase of $34,000 in sales d. increase of $1 in advertising is associated with an average increase of $4,000 in sales
D
In a regression analysis if R2 = 1, then a. SSE = SST b. SSE = 1 c. SSR = SSE d. SSR = SST
D
Regression analysis was applied to analyze the relationship between demand for a product (y) and the price of the product (x), and the following estimated regression equation was obtained: y^ = 120-10x Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to on average a. increase by 120 units b. increase by 100 units c. increase by 20 units d. decrease by 20 units
D
Which distribution is used to test the significance of the population coefficient of determination? a. standard normal distribution b. Student's t distribution with df = n - 1 c. Student's t distribution with df = n - 2 d. F-distribution
D
Which of the following measures the amount of dispersion of observed data around a regression line? a. correlation coefficient b. coefficient of determination c. standard error of the slope d. standard error of the estimate
D
Which of the following measures the total variation in the dependent variable in simple regression analysis? a. standard error b. sum of squares error c. sum of squares regression d. total sum of squares
D
