Based on this data what is the R Square

Question

14, 25, 15, 5, 10, 12, 5, 21

GPA: 3.1, 3.7, 3.4, 3.0, 3.1, 3.3, 2.7, 3.8

Answer 1

You didn't name the first variable. I assume it is the other half of the bi-variate data. I will call the first variable AST as the values would fit.

There are several ways to do a regression and calculate R² , you should look into them as they are straight forward with such a small dataset as this.

Follow this link: https://www.statology.org/calculate-r-squared-by-hand/

This is the purpose of the homework, learning by doing. Take the data, create the necessary table in excel and then do the calculations by row. Finally follow the formula to calculate the R² hint: it has to do with the sum of the square of the errors and the total sum of the square.

That being said, I used R to solve the linear equation

AST = c(14, 25, 15, 5, 10, 12, 5, 21)

GPA = c(3.1, 3.7, 3.4, 3.0, 3.1, 3.3, 2.7, 3.8)

gpa.model <- lm(GPA~AST)

summary(gpa.model)

The results were as follows. (use to check your own hand work)

Call:

lm(formula = GPA ~ AST)

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 2.623616 0.122041 21.50 6.61e-07 ***

AST. 0.047767 0.008179 5.84 0.00111 **

Residual standard error: 0.153 on 6 degrees of freedom

Multiple R-squared: 0.8504, Adjusted R-squared: 0.8255