Exam 12: Linear Regression and Correlation

Data is collected from 20 sales people in order to verify that the more contacts made with potential clients, the greater the sales volume. The Excel printout is shown below. This model predicts that with 25 sales contacts, sales will be:

The partial Mega Stat output below is regression analysis of the relationship between annual payroll and number of wins in a season for 28 teams in professional sports. The purpose of the analysis is to predict the number of wins when given an annual payroll in $millions. Although technically not a sample, the baseball data below will be treated as a convenience sample of all major league professional sports. Refer to the printout above. How many independent variables?

i. If the coefficient of correlation is 0.80, what is the coefficient of determination? ii. What is a measure of the scatter of observed values around the regression line called? iii. If the correlation between sales and advertising is + 0.6, what percent of the variation in sales can be attributed to advertising?

Given the following five points: (-2,0), (-1,0), (0,1), (1,1), and (2,3). What is the slope of the line?

i. In order to visualize the form of the regression equation, we can draw a scatter diagram. ii. The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y. iii. In regression analysis, the predicted value of Y' rarely agrees exactly with the actual Y value, i.e., we expect some prediction error.

We have collected price per share and dividend information from a sample of 30 companies. The slope in this instance indicates:

Which of the following statements regarding the coefficient of correlation is true?

Which of the following is NOT a difference between a confidence interval and a prediction interval?

Which value of r indicates a stronger correlation than -0.40?

The relationship between interest rates as a percent (X) and housing starts (Y) is given by the linear equation Y' = 4094 - 269X. What happens to housing starts as interest rates fall?

The partial mega stat output below is regression analysis of the relationship between annual payroll and number of wins in a season for 28 teams in professional sports. The purpose of the analysis is to predict the number of wins when given an annual payroll in $millions. Although technically not a sample, the baseball data below will be treated as a convenience sample of all major league professional sports. Refer to the printout above. The regression equation is:

i. If there is absolutely no relationship between two variables, what will Pearson's r equal? ii. If the value of r is -0.96, what does this indicate about the dependent variable as the independent variable increases? iii. What is the value of the correlation coefficient if there is perfect correlation?

The correlation between two variables is 0.29 for a sample of 12 observations. Based on a null hypothesis of no correlation versus an alternative hypothesis of positive correlation, what conclusion may be drawn at the.05 level of significance?

What is the measure that indicates how precise a prediction of Y is based on X or, conversely, how inaccurate the prediction might be?

i. The coefficient of determination can only be positive. ii. If the coefficient of correlation is 0.68, the coefficient of determination is 0.4624. iii. The standard error of estimate measures the accuracy of our prediction.

A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected: The y-intercept in this instance suggests:

i. The technique used to measure the strength of the relationship between two sets of variables using the coefficient of correlation and the coefficient of determination is called regression analysis. ii. In order to visualize the form of the regression equation, we can draw a scatter diagram. iii. When a regression line has a zero slope, indicating a lack of a relationship, the line is horizontal to the x-axis.

i. In order to visualize the form of the regression equation, we can draw a scatter diagram. ii. When a regression line has a zero slope, indicating a lack of a relationship, the line is vertical to the x-axis. iii. In regression analysis, the predicted value of Y' rarely agrees exactly with the actual Y value, i.e., we expect some prediction error.

i. A coefficient of correlation close to 0 (say, 0.08) shows that the relationship between two variables is quite weak. ii. A coefficient of correlation of -0.96 indicates a very weak negative correlation. iii. The coefficient of determination can only be positive.

Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Excel results are summarized below: From this printout you determine: