List of top Statistics Questions on Regression Analysis

Consider the multiple linear regression model
\[ Y_i = \beta_0+\beta_1 x_{i1}+\beta_2 x_{i2}+\beta_3 x_{i3}+\epsilon_i, \quad i=1,2,\ldots,31, \]
where \(\epsilon_i\) are iid \(N(0,1)\) variables. The \(F\)-test for testing significance of regression rejects \(H_0: \beta_1=\beta_2=\beta_3=0\) at \(5\%\) level. Given \[ F_{0.05;3,27}=2.96,\quad F_{0.05;3,30}=2.92,\quad F_{0.025;3,27}=4.01,\quad F_{0.025;3,30}=3.91. \] Then the value of \(R^2\) cannot be equal to

If \(Y = mX + 4\) and \(X = 4Y + 5\) are the regression lines of Y on X and X on Y respectively, then m lies between the values:

The data below are the temperatures on randomly chosen days during the summer and the number of employee absences at a local company on those days. What is the 95% confidence interval about the slope of the true least-squares regression line, for the data given below?