Exam 12: Linear Regression and Correlation

i. The purpose of correlation analysis is to find how strong the relationship is between two variables. ii. A coefficient of correlation of -0.96 indicates a very weak negative correlation. iii. The standard error of estimate measures the accuracy of our prediction.

i. In order to visualize the form of the regression equation, we can draw a scatter diagram. ii. In regression analysis, the predicted value of Y' rarely agrees exactly with the actual Y value, i.e., we expect some prediction error. Iii) 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.

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

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:

If the decision in the hypothesis test of the population correlation coefficient is to reject the null hypothesis, what can we conclude about the correlation in the population?

A scatter diagram is a chart

What is the range of values for a coefficient of correlation?

-What is the meaning of a negative slope?

i. Correlation analysis is a group of statistical techniques used to measure the strength of the relationship (correlation) between two variables. Ii) A correlation coefficient of -1 or +1 indicates perfect correlation. Iii) The strength of the correlation between two variables depends on the sign of the coefficient of correlation.

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) A line found using the least squares principle is the best-fitting line because the sum of the squares of the vertical deviations between the actual and estimated values is minimized.

What is the chart called when the paired data (the dependent and independent variables) are plotted?

i. Trying to predict weekly sales with a standard error of estimate of $1,955, we would conclude that 68 percent of the predictions would not be off more than $1,955, 95 percent would not be off by more $3,910, and 99.7 percent would not be off by more than $5,865. Ii) Approximately 68% of the values lie within one standard error of the regression line Iii) For a set of observations, there is no difference in the width of a confidence interval and the width of a predictor interval.

The partial megastat 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. The coefficient of correlation is a measure of the strength of relationship between two variables. ii. The coefficient of determination can only be positive. Iii) The standard error of estimate measures the accuracy of our prediction.

The partial megastat 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. Predict the number of wins for a team with PAYROLL = 25(million) (nearest whole number)

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.

The partial megastat 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 critical value of t, at the 5% level of significance, for testing the coefficient of correlation is:

Given the scatter diagram below, that shows the number of workdays absent per year based on the age of the employees, which of the following statements are true?

A regression analysis yields the following information: Y' = 2.24 + 1.49 X S y x = 1.66; ∑x = 32; ∑x2 = 134; n = 10 Estimate the value of Y' when X = 4.

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?