# DSC 670 Regression Study

DSC 670 Assignment  9

1. Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable).

 x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2

 a. Develop the least squares estimated regression equation. b. At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. c. Perform an F test to determine whether or not the model is significant. Let a = 0.05. d. Compute the coefficient of determination.

1. Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel to develop a scatter diagram and to compute the least squares estimated regression equation.

 x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2

1. A company has recorded data on the daily demand for its product (y in thousands of units) and the unit price (x in hundreds of dollars). A sample of 11 days demand and associated price resulted in the following data.

 å x = 154 å x 2 = 2,586 å y = 451 å y 2 = 18,901 å x y = 5,930

 a. Using the above information, develop the least-squares estimated regression line. b. Compute the coefficient of determination. c. Perform an F test and determine whether or not there is a significant relationship between demand and unit price. Let a = 0.05. d. Perform a t test to determine whether the slope is significantly different from zero. Let a = 0.05. e. Would the demand ever reach zero? If yes, at what price would the demand be zero? Show your complete work.

1. Shown below is a portion of a computer output for a regression analysis relating y (dependent variable) and x (independent variable).

 ANOVA df SS Regression 1 50.58 Residual 13 55.42 Total 14 106.00 Coefficients Standard Error t Stat Intercept 16.156 1.42 Variable x -0.903 0.26

 a. Perform a t test and determine whether or not y and x are related. Use a = 0.05. b. Compute the coefficient of determination and fully interpret the meaning. Be very specific.

1. Shown below is a portion of a computer output for regression analysis relating y (dependent variable) and x (independent variable).

 ANOVA df SS Regression 1 882 Residual 20 4000 Total 21 4882 Coefficients Standard Error t Stat Intercept 5.00 3.56 Variable x 6.30 3.00

 a. What has been the sample size for the above? b. Perform a t-test and determine whether or not x and y are related. Use a = 0.05. c. Perform an F-test and determine whether or not x and y are related. Use a = 0.05. d. Compute the coefficient of determination. e. Interpret the meaning of the value of the coefficient of determination that you found in d. Be very specific.

1. Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel’s Regression Tool to answer the following questions.

 x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2

 a. What is the estimated regression equation? b. Perform a t test and determine whether or not x and y are related. Use a = 0.05. c. Perform an F test and determine whether or not x and y are related. Use a = 0.05. d. Find and interpret the coefficient of determination.

1. A company has recorded data on the weekly sales for its product (y) and the unit price of the competitor’s product (x). The data resulting from a random sample of 7 weeks follows. Use Excel’s Regression Tool to answer the following questions.

 Week Price Sales 1 .33 20 2 .25 14 3 .44 22 4 .40 21 5 .35 16 6 .39 19 7 .29 15

 a. What is the estimated regression equation? b. Perform a t test and determine whether or not x and y are related. Use a = 0.05. c. Perform an F test and determine whether or not x and y are related. Use a = 0.05. d. Find and interpret the coefficient of determination.

1. Coyote Cable has been experiencing an increase in cable service subscribers in recent months due to increased advertising and an influx of new residents to the region.  The number of subscribers (in 1000’s) for the last 16 months are as follows:

 Month Sales Month Sales Month Sales 1 12.8 7 20.6 12 23.8 2 14.6 8 18.5 13 25.1 3 15.2 9 19.9 14 24.7 4 16.1 10 23.6 15 26.5 5 15.8 11 24.2 16 28.9 6 17.2

Using simple linear regression, forecast the number of subscribers for months 17, 18, 19, and 20.

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