A student in an intro stats course collects data at her university. she wants to model the relationship between student jobs and

Question

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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?

Mathematics

2 answers:

zzz [12.3K] · Answer 1 · 2026-03-17T12:28:54+03:00

Response:

12.7% of the variation in GPA can be attributed to the number of hours worked

Detailed explanation:

$R^2$ This plays a crucial role in linear regression.

$R^2$ explains variance, essentially demonstrating the variation in the model, while our objective is to reduce residuals.

It provides insight into the change in the dependent variable triggered 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 identifies GPA as the dependent variable and number of working hours as the independent variable.

$R^2$ = 12.7%

This implies that 12.7% change in the dependent variable is explicable by the independent variable, meaning 12.7% of changes in GPA can be accounted for by the number of working hours

.

babunello [11.8K] · Answer 2 · 2026-03-17T12:25:13+03:00

Response:

We are provided with:

$R^{2}=12.7\%$

The interpretation of $R^{2}$ signifies the extent of variation in the response variable accounted for by the explanatory variable within the model

Thus, the interpretation of $R^{2}=12.7\%$ indicates that 12.7% of the variation in the GPA response variable is attributed to the job-related explanatory variable in the specified linear regression model.