Question

sat reading score, x | 497 | 515 | 518 | 592 | 568 | 572 | 543 | 501 | 522
sat math score, y | 510 | 515 | 523 | 587 | 535 | 554 | 529 | 514 | 521
a) this data has a significant correlation. create a scatterplot of the data and include the regression line and equation on your plot. insert your plot here:
sat reading score vs. sat math score
b) use your regression equation to predict the y - value for x = 550, and write a sentence interpreting this prediction in the context of the data

Explanation:

Step1: Substitute \(x = 550\) into the regression equation

The regression equation is \(y=0.46x + 178\).
Substitute \(x = 550\) into the equation: \(y=0.46\times550+178\).

Step2: Calculate the value of \(y\)

First, calculate \(0.46\times550\): \(0.46\times550=(0.4 + 0.06)\times550=0.4\times550+0.06\times550 = 220+33=253\).
Then, add \(178\) to the result: \(y = 253+178=431\).

Answer:

When \(x = 550\) (the SAT Reading Score), the predicted \(y\)-value (SAT Math Score) is \(431\). This means that based on the regression model of the given data, a student with an SAT Reading Score of \(550\) is predicted to have an SAT Math Score of \(431\).