Regression Analysis
Regression Analysis Exercises
1- A farmer wanted to find the relationship between the amount of fertilizer used and the yield of corn. He selected seven acres of his land on which he used different amounts of fertilizer to grow corn. The following table gives the amount (in pounds) of fertilizer used and the yield (in bushels) of corn for each of the seven acres.
|Fertilizer Used |Yield of Corn |
|120 |138 |
|80 |112 |
|100 |129 |
|70 |96 |
|88 |119 |
|75 |104 |
|110 |134 |
a. With the amount of fertilizer used as an independent variable and yield of corn as a dependent variable, compute SSxx, SSyy, and SSxy. b. Find the least squares regression line. c. Interpret the meaning of the values of a and b calculated in part b. d. Calculate r and r2 and explain what they mean. e. Compute the standard deviation of errors. f. Predict the yield of corn per acre for x = 105. g. Construct a 98% confidence interval for ß. h. Test at the 5% significance level if ß is different from zero.
1- A farmer wanted to find the relationship between the amount of fertilizer used and the yield of corn. He selected seven acres of his land on which he used different amounts of fertilizer to grow corn. The following table gives the amount (in pounds) of fertilizer used and the yield (in bushels) of corn for each of the seven acres.
|Fertilizer Used |Yield of Corn |
|120 |138 |
|80 |112 |
|100 |129 |
|70 |96 |
|88 |119 |
|75 |104 |
|110 |134 |
a. With the amount of fertilizer used as an independent variable and yield of corn as a dependent variable, compute SSxx, SSyy, and SSxy. b. Find the least squares regression line. c. Interpret the meaning of the values of a and b calculated in part b. d. Calculate r and r2 and explain what they mean. e. Compute the standard deviation of errors. f. Predict the yield of corn per acre for x = 105. g. Construct a 98% confidence interval for ß. h. Test at the 5% significance level if ß is different from zero.