Linear Regression Results The REG Procedure
Model: Linear_Regression_Model
Dependent Variable: Y
Analysis of Variance
Source DF Sum of Mean F Value Pr > F
Squares Square
Model 1 113.15714 113.15714 46.78 0.0024
Error 4 9.67619 2.41905
Corrected
Total 5 122.83333
Root MSE 1.55533 R-Square 0.9212
Dependent
Mean 11.83333 Adj R-Sq 0.9015
Coeff Var 13.14362
Parameter Estimates
Variable DF Parameter Standard t Value Pr > |t| 95% Confidence
Estimate Error Limits
Intercept 1 -7.23810 2.85984 -2.53 0.0646 -15.17828 0.70209
X 1 2.54286 0.37179 6.84 0.0024 1.51059 3.57512
Generated by the SAS System (Local, XP_PRO) on 29JUN2010 at 8:33 AM
X Y predicted_Y lclm_Y uclm_Y lcl_Y ucl_Y residual_Y
5 7 5.476190476 2.350845 0.601536 0.145584 10.8068 1.52381
6 8 8.019047619 5.672672 10.36542 3.104471 12.93362 -0.01905
7 9 10.56190476 8.724971 12.39884 5.869154 15.25466 -1.5619
8 12 13.1047619 11.26783 14.9417 8.412011 17.79751 -1.10476
9 15 15.64761905 13.30124 17.99399 10.73304 20.5622 -0.64762
10 20 18.19047619 15.06513 21.31582 12.85987 23.52108 1.809524
At a local department store, let X be an independent variable for the number of salespeople on the floor and y the dependent variable for daily sales in thousands of dollars. The next screen will present the data.
X={5, 6, 7, 8, 9, 10} Y = {7, 8, 9, 12, 15, 20}
Steps to using PC-SAS for the above problem.
1. Click on start -- go to programs -- go to SAS -- go to Enterprise Guide 4.0
a. Click on new data
b. type a name in the appropriate box and then click save
c. Change A to X
d. Change type to numeric
e. repeat this procedure changing B to Y
d. click on finish
2. You now see a spreadsheet.
a. enter the data. In row 7 column x enter the number 4
b. if you have rows with dots only then highlight them and delete them.
3. Go up to the menu on the top row and click Analyze and drag down to Regression and over to Linear. Click yes to continue
4. Click on X then click on the right arrow and then click on explanatory variables
a. Click on Y then click on the right arrow and then click on dependent variables
5. Click on statistics then click on confidence limits for parameter estimates and leave at 95%
6. Click on predictions and then click on original sample and residual and prediction limits.
7. Click on titles then click on Use default text (to uncheck it and write your own). Then click in the big box and type the name of the worksheet and your name or names.
8. Then click run (this "submits" or "runs" the program).
9. Then you will see an analysis window. Then print this page using the print command.
10. Then on the left side under Project Explorer, double click on Linear regression predictions and statistics for (the file name you give it). If you have blank columns you may delete them after going up to data and dragging down to read only. There are two columns you will not need. Thus you can delete the last 2 columns. Then print this table.
11. An optional way to print is go up to file and drag down to send to and over to either excel or word. Then print from that file.
1. Write down the prediction equation.
2. Write down SSE, S2, SSyy and S(std. dev).
3. Predict the retail sales when there are 10 salespeople on the floor and then calculate the prediction error.
4. Construct a 95% confidence interval for b1.
5. Test if the number of salespeople on the floor is significant to the prediction of y.
6. Find the coefficient determination and interpret.
7. Find the 95% confidence interval for E(Y) when x = 10 salespeople.
8. Find a 95% prediction interval for Y when x = 10 salespeople.
9. Predict Y if x = 4 salespeople and find the confidence interval for E(y) and the prediction interval for Y. Is there a residual? If not, why not? If yes then what is it?
You must use either Mini Tab, Excel or SAS to answer all these questions.
1. Write down the prediction equation.
2. Write down SSE, S2, SSyy and S(std. dev).
3. Predict the retail sales when there are 10 salespeople on the floor and then calculate the prediction error.
4. Construct a 95% confidence interval for b1.
5. Test if the number of salespeople on the floor is significant to the prediction of y.
6. Find the coefficient determination and interpret.
7. Find the 95% confidence interval for E(Y) when x = 10 salespeople.
8. Find a 95% prediction interval for Y when x = 10 salespeople.
9. Predict Y if x = 4 salespeople and find the confidence interval for E(y) and the prediction interval for Y. Is there a residual? If not, why not? If yes then what is it?