a mathematics professor wishes to analyze the relationship between the number of papers graded by his department's student homework graders an the total amount of money paid to the graders. He collects data for 12 randomly chosen graders and uses MINITAB to do the regression analysis. Below is a portion of the minitab output. (Here, COST= amount paid (dollars), PAPERS = number of papers in hundreds, and the intervals listed at the bottom are computed for 1600 papers.)

Regression equation is COST = 35.8+12.1 PAPERS
Predictor Coed Std.dev t-ratio p
Constant 35.8 17.06 2.1 .062
PAPERS 12.0835 .9738 12.41 .0000

s=6.526 r-sq= 93.9% r-sq(adj)= 93.3%

To analyze the relationship between the number of papers graded and the total amount of money paid to the graders, the mathematics professor used regression analysis in MINITAB. The regression equation is given as:

COST = 35.8 + 12.1 PAPERS

This equation shows that the estimated cost is equal to 35.8 plus 12.1 times the number of papers.

Let's break down the MINITAB output:

1. Predictor: This column lists the predictor variables in the regression analysis. In this case, the predictor variable is the number of papers graded (PAPERS).

2. Coef: Coefficient estimates for the predictors. For the constant term, the coefficient is 35.8, and for the PAPERS variable, the coefficient is 12.1.

3. Std.dev: Standard deviation of the coefficient estimates. For the constant term, the standard deviation is 17.06, and for the PAPERS variable, the standard deviation is 0.9738.

4. t-ratio: The t-ratio measures the number of standard deviations the coefficient is from zero. For the constant term, the t-ratio is 2.1, and for the PAPERS variable, the t-ratio is 12.41.

5. p: The p-value represents the probability of observing a coefficient as extreme as the one estimated if the null hypothesis is true (null hypothesis being that the coefficient is equal to zero). For the constant term, the p-value is 0.062, and for the PAPERS variable, the p-value is 0.0000.

6. s: The s value is the estimated standard deviation of the residuals (errors) in the regression model. In this case, s is equal to 6.526.

7. r-sq: The coefficient of determination (r-squared) measures the proportion of the variability in the dependent variable (COST) that can be explained by the independent variable (PAPERS). In this case, r-squared is 93.9%, indicating that 93.9% of the variability in COST can be explained by PAPERS.

8. r-sq(adj): Adjusted r-squared takes into account the number of predictor variables in the model. In this case, the adjusted r-squared is 93.3%.

Based on the MINITAB output, the professor can conclude that there is a significant relationship between the number of papers graded and the total amount of money paid to the graders. The regression equation can be used to estimate the cost based on the number of papers graded, and the model explains a large amount of the variability in the cost.