The problem states:
In an Economics class, midterm scores average out to 75 with a standard deviation of 15, so does the scores on the final. The correlation between midterm scores and final scores is 0.5. Use the given information to estimate the average final score for the students whose midterm scores were 80.
I know beta 1 can be estimated by the sample covariance of (X,Y) over the Sample var of X. If I can find beta 0 as well, I have a full estimated linear regression equation and can plug in to get my estimates from there. How would I develop this equation with the information given.
Let $Y_i$ be final exam scores and $X_i$ be midterm scores. The regression line must pass through the point $(\bar X, \bar Y),$ so $\bar Y = \hat \beta_0 + \hat \beta_1 \bar X.$ You say you know all the values in this equation except for $\hat \beta_0.$ Solve.