Question

Heidi collected data about the mileage (in thousands of kilometers) and value (in thousands of dollars) for a random sample of 11 cars of the same make and model. The data showed a strong negative linear relationship. Based on a least-squares regression analysis on her sample, the computer output is as follows:

Predictor Coefficient: 39.575
Standard Error of Coefficient: 0.765
T-Value: 51.77
P-Value: 0.00

Mileage Coefficient: -0.246
Standard Error of Coefficient: 0.013
T-Value: -18.87
P-Value: 0.00

What is the coefficient of determination (R-squared) for the regression analysis?
1) 1.349
2) 97.26
3) 39.575
4) -0.246

Answer 1

The coefficient of determination (R-squared) cannot be determined from the given coefficients and p-values, as it is not provided directly in the output and requires additional statistical output to calculate. Moreover, none of the provided options are valid for R-squared since it ranges between 0 and 1.

Step-by-step explanation:

The coefficient of determination, commonly denoted as R-squared (R²), is used in the context of a regression analysis to measure the percentage of the variance in the dependent variable that is predictable from the independent variable(s). R² is the square of the correlation coefficient (r), and it provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.

In the provided computer output, the p-values for both the predictor and mileage coefficients are 0.00, which suggests a strong significance of the variables in the regression model. However, to find the R-squared value, one would typically look for it directly in the output from the statistical software. As R-squared is not explicitly provided here and cannot be calculated solely based on the provided coefficients and p-values, we can't determine the exact R-squared value from the given data. All listed options (1.349, 97.26, 39.575, -0.246) are not valid values for R² since R² is always between 0 and 1 (or 0% and 100% when expressed as a percentage).

The general understanding is that R-squared values cannot be negative, as they represent a proportion of variance explained by the model, and proportions cannot be negative.