 gainejavima

2021-11-17

Find the GPA of a student if he gives average hours to study by using regression alysis. A random sample of ten students is selected from a class of 60 students, find regression line and also find the GPA of a student if he gives average hours to study by using this regression analysis. Their GPA and the hours to study are given below:

Also interpret the regression coefficient. Elizabeth Witte

Step 1
In simple linear regression, there will be exactly one dependent variable and independent variable.
Step 2
The regression analysis can be done in any of the statistical software or by hand. Here GPA is the dependent variable (X) and amount of time study is the independent variable (Y).
So the regression line can be calculated as follows.
Sum of $X=49$
Sum of $Y=31.1$
$X=49$
$Y=3.11$
Sum of squares $SSX=34,9$
Sum of products =7.51

=0.21519
$a=Y-bX$
=2.05559
So the regression equation is given below.
$\stackrel{^}{y}$ = 2.05559 + 0.21519X
Step 3
Here the average hours of study is 4.9. Substitute this in the regression equation.
$\stackrel{^}{y}=2.05559+0.21519\left(4.9\right)$
=3.11
So the GPA is 3.11 when the the study time is average.
Her the regression coefficient is 0.21519. This indicates that for every one unit change in time, the GPA also change by 0.21519 in the same direction.

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