A survey is conducted on 700 Californians older than 30 years of age. The study wants to obtain inference on the relationship between years of education and yearly income in dollars. The response variable is income and the explanatory variable is years of education.

A simple linear regression model is fit, and the output from R is below:

lm(formula = Income ~ Education, data = CA) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 25200.20 1488.94 16.93 3.08e-10 *** Education 2905.35 112.61 25.80 1.49e-12 ***

Residual standard error: 32400 on 698 degrees of freedom Multiple R-squared: 0.7602

a.

Write out the estimated linear equation. Round to two decimal places, x.xx

Income_i=_________+__________Education_i

_b. Assume someone can have 0 years of education. Does the intercept have a useful interpretation? And if so, what is that interpretation?

a. No useful interpration.

b. Yes, it is the estimated expected income of someone with 1 years of education.

c. Yes, it is the estimated expected income of someone with 0 years of education.

d. Yes, it is the estimated expected income of someone with the most years ofeducation.

c.

Say we have two people, where person 1 has 5 years more education than person 2. How much more income do we estimate person 1 to make compared to person 2?

Round to the nearest 2nd decimal place, x.xx

d.

As a person increases their years of education by 1 unit (1 year), how much do we estimate their expected income to increase? Round to the nearest 2nd decimal place, x.xx