Question

Thirteen students entered the business program at Sante Fe College 2 years ago. The following table indicates what each student scored on the high school SAT math exam and their​ grade-point averages​ (GPAs) after students were in the Sante Fe program for 2 years.
Student A B C D E F G
SAT Score 421 375 585 693 608 392 418
GPA 2.93 2.87 3.03 3.42 3.66 2.91 2.12
Student H I J K L M
SAT Score 484 725 506 613 706 366
GPA 2.50 3.24 1.97 2.73 3.88 1.58 ​
The​ least-squares regression equation that shows the best relationship between GPA and the SAT score is:________ ​(round your responses to four decimal ​places)​

Answer 1

Answer:

ŷ = 0.0035X + 1.0030

Explanation:

Given the data :

Student A B C D E F G H I J K L M

SAT Score: 421 375 585 693 608 392 418 484 725 506 613 706 366

GPA: 2.93 2.87 3.03 3.42 3.66 2.91 2.12 2.50 3.24 1.97 2.73 3.88 1.58 ​

We can obtain the Least square regression calculator, we can obtain the least square regression equation in the Format :

y = mx + c

Where ; m = gradient / slope

x = predictor variable ; c = intercept

y = Independent variable.

The model equation produced by the calculator is :

ŷ = 0.0035X + 1.0030

y predicted variable ; x = explanatory variable

0.0035 = slope or gradient ; 1.0030 = intercept