Give the formulas for the ols estimates of β 0 and β 1 in the simple linear regression model with the Y and X as specified in this problem. Interpret the estimates. Find the fitted values and the...

Give the formulas for the ols estimates of β₀
and β₁
in the simple linear regression model with the Y and X as specified in this problem. Interpret the estimates.

Find the fitted values and the residuals. Give an expression for RSS obtained by squaring and adding up the residuals and then dividing by the df.

Show that the t-statistic for testing β1 = 0 is exactly the same as the usual two-sample t-test for comparing two groups with an assumption of equal within-group variance.