Question

Did the estimated regression equation provide a good fit?

a. yes, it provides a good fit as 82% of the variation in y is explained by the model
b. no, it does not provide good fit because the size of the sample is smaller than 30
c. yes, it provides a good fit because both coefficients are statistically significant
d. there is no evidence to make conclusions about the fitness of the model

Answer 1

The
`R^2` value of 0.82 indicates that approximately 82% of the variation in the dependent variable (monthly maintenance) is explained by the regression model.

Option c. "Yes, it provides a good fit as 82% of the variation in y is explained by the model" is the correct answer.

Did the estimated regression equation provide a good fit?

The coefficient of determination, denoted as
`R^2`, is a statistical measure that represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s) in a regression model. It ranges from 0 to 1, with a higher value indicating a better fit of the regression model to the data.

In this case, an
`R^2`value of 0.82 means that 82% of the variation in the monthly maintenance can be explained by the independent variable(s) included in the regression model.

This suggests that the estimated regression equation, y = 6.1092 + 0.8951x, provides a good fit to the data, as a significant portion of the variability in monthly maintenance is accounted for by the relationship with the predictor variable(s).

ANOVA

df SS

Regression 1 1575.76

Residual 8 349.14

Estimated regression equation is y =6.1092+0.8951x

T-Calculated is 6.007

Based on the value of the t-test and on this regression results usage is significant to explain the changes on monthly maintenance.

Total 9 1924.90

Coefficients Standard Error

Intercept 6.1092 .9361

Usage 0.8951 .149

The estimated regression equation is y = 6.1092 + 0.8951 x

T-test calculated is 6.007

Based on the value of the t-test and on the regression results, usage is significant to explain the changes in monthly maintenance.

F-Calculated is 36.11

The model as a whole is significant, we reject the null hypothesis.

R^2 value is 0.82

Did the estimated regression equation provide a good fit?

a. There is no evidence to make conclusions about the fitness of the model

b. Yes, it provides a good fit because both coefficients are statistically significant

c. Yes, it provides a good fit as 82% of the variation in y is explained by the model

d. No, it does not provide good fit because the size of the sample is smaller than 30