Question

Researchers have created a prediction equation to predict a state’s average SAT score (Y’) using the percentage of HS seniors who take the SAT as their predictor variable (X). The prediction equation has a slope of -2.5 and a y-intercept of 510. Knowing that 30 percent of all high school seniors in Wisconsin take the SAT, you predict Wisconsin’s average SAT score to be __________; if Wisconsin actually has an average SAT score of 460, you calculate a prediction error of _________.

Answer 1

Answer:

a) 435 average SAT score

b) 25        

Step-by-step explanation:

We are given the following in the question:

State’s average SAT score(y') is the dependent variable and percentage of HS seniors(x) is the independent variable.

Slope, m  = -2.5

y-intercept, c = 510

We can write the regression equation as:

$y'(x) = mx + c\\y'(x) = -2.5x + 510$

Predicted SAT score when 30 percent of all high school seniors in Wisconsin take the SAT.

We put x = 30

$y'(30) = -2.5(30) + 510 = 435$

Thus, the average SAT score would be 435.

Actual average SAT score = 460

Prediction Error =

$=\sqrt{\dfrac{(435-460)^2}{1}} = 25$