1. Text Exercise 4.43 (a) 1 for level A X = 0 otherwise Y =  0 +  1 X +  or E(Y) =  0 +  1 X  0 =  1 = the mean of Y for level B the amount that the mean of Y for level A exceeds the mean of Y for level B Do this by first defining the appropriate dummy variable(s), then writing a regression model, and finally writing a statement interpreting each parameter in the model. Homework #16Score____________/ 10Name ______________

2. (b) 1 for level A X 1 = 0 otherwise Y =  0 +  1 X 1 +  2 X 2 +  3 X 3 +  or E(Y) =  0 +  1 X 1 +  2 X 2 +  3 X 3  0 =  1 =  2 =  3 = the mean of Y for level D the amount that the mean of Y for level A exceeds the mean of Y for level D Do this by first defining the appropriate dummy variable(s), then writing a regression model, and finally writing a statement interpreting each parameter in the model. 1 for level B X 2 = 0 otherwise 1 for level C X 3 = 0 otherwise the amount that the mean of Y for level B exceeds the mean of Y for level D the amount that the mean of Y for level C exceeds the mean of Y for level D

3. Additional HW Exercise 5.1 (a) (b) A study is being conducted to see if corn yield in bushels per acre can be predicted from monthly rainfall in inches and average daily temperature in O F. Data observed on several randomly selected farms has been stored in the SPSS data file corn. yld =  0 +  1 (rain) +  2 (temp) +  Write a first-order model for the prediction of corn yield from monthly rainfall and average daily temperature. Use the Analyze > Regression > Linear options in SPSS to obtain SPSS output displaying the ANOVA table and coefficients in the least squares prediction equation for the first-order model in part (a). To have the mean and standard deviation displayed for the dependent and independent variables, click on the Statistics button, and select the Descriptives option. Title the output to identify the homework exercise (Additional HW Exercise 5.1 - part (b)), your name, today’s date, and the course number (Math 214). Use the File > Print Preview options to see if any editing is needed before printing the output. Attach the output to this assignment before submission.

4. (c) Summarize the results (Step 4) of the f test to see if there is sufficient evidence that the prediction of corn yield from monthly rainfall and average daily temperature is significant at the 0.05 level. Since f 2,21 = 3566.914 and f 2,21;0.05 = 3.47, we have sufficient evidence to reject H 0. We conclude that the prediction of corn yield from monthly rainfall and average daily temperature is significant (P < 0.01). OR (P < 0.001)

5. Additional HW Exercise 5.1 - continued (d) (e) In order to see if we can improve prediction, the complete second order model is now considered. Write a complete second-order model for the prediction of corn yield using the complete second order model with independent variables rainfall and temperature. yld =  0 +  1 (rain) +  2 (temp) +  12 (rain)(temp) +  11 (rain) 2 +  22 (temp) 2 +  Use SPSS to create three new variables, one named raintemp equal to the product of the variables rainfall and temperature, one named rain2 equal to the square of rainfall, and one named temp2 equal to the square of temperature. Use the Analyze > Regression > Linear options in SPSS to obtain SPSS output displaying the ANOVA table and coefficients in the least squares prediction equation for the complete second-order model in part (d). Since you only need the ANOVA table and the coefficients in the least squares prediction equation, you may choose to delete all other sections of the SPSS output. Title the output to identify the homework exercise (Additional HW Exercise 5.1- part (e)), your name, today’s date, and the course number (Math 214). Use the File > Print Preview options to see if any editing is needed before printing the output. Attach the output to this assignment before submission.

6. (f) Summarize the results (Step 4) of the f test to see if there is sufficient evidence that the prediction of corn yield using the complete second order model with independent variables rainfall and temperature is significant at the 0.05 level. Since f 5,18 = 15482.454 and f 5,18;0.05 = 2.77, we have sufficient evidence to reject H 0. We conclude that the prediction of corn yield using the complete second order model with independent variables rainfall and temperature is significant (P < 0.01). OR (P < 0.001)