Question

A student in an intro stats course collects data at her university. she wants to model the relationship between student jobs and gpa. she collects a random sample of students and asks each for their gpa and the number of hours per week they work. she checks the conditions and makes a linear model with gpa as the response variable. she finds that the​ r-squared statistic is​ 12.7%. what is the correct interpretation of this​ number?

Answer 1

Answer:

12.7% changes in gpa can be accounted because of number of working hours    

Step-by-step explanation:

$R^2$  plays an important role in the linear regression.

$R^2$ explain variance, basically it explains the variation in the model, and our aim is to minimize the residuals.

It explains the change in the dependent variable cause by the independent variable.

Formula:

$R^2 = \frac{\text{Explained}}{\text{Total Variation}} = \frac{\text{Sum of squares of regression}}{\text{Total variation}} = \frac{\text{1 - Sum of squares of residuals}}{\text{Total variation}}$

The student says that gpa is the dependent variable and and number of working hour is the independent cariable.

$R^2$ = 12.7%

This means 12.7% change in the dependent variable is explained by the independent variable that is 12.7% changes in gpa can be accounted because of number of working hours

.

Answer 2

Answer:

We are given:

$R^{2}=12.7\%$

The interpretation of $R^{2}$ is the amount of variation in response variable that is explained by the explanatory variable in the model

Therefore, the interpretation of $R^{2}=12.7\%$ is 12.7% of variation in gpa response variable is explained by the jobs explanatory variable in the given linear regression model.