1. Find the L²-regression line for the points (1, 2), (3, 4), (5,8) in the plane.

The Simple Linear Regression model is   Y = b0 + b1*X1 + u   and the Multiple Linear Regression model with k variables is:   Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u   Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term,   Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 28 Suppose your estimated MLR model is: Y_hat = -30 + 2*X1 + 10*X2 Suppose the standard error for the estimated coefficient associated with X2 is equal to 5. Now, suppose that for some reason we multiply X2 by 5 and we re-estimate the model using the rescaled explanatory variable. What will be the value of the estimated coefficient of X2 and its standard error?   The estimated coefficient of X2 will be equal to 50 and its standard error will be…

4. Our R² implies that lots of stuff, other than health, also affects doctor visits. One such thing is a person's insurance status. The data file includes a third variable that records whether the person had health insurance during 2019. Estimation a regression of the form y = Bo + B₁x1 + B₂x₂ where x₁ is the health status variable from above, but now x₂ records whether the person had insurance. a) Interpret the estimate of B₁ in words. b) Interpret the estimate of B₂ in words. c) Forecast a person's number of doctor visits in 2019 if he/she was in excellent health, but did not have insurance. d) Forecast a person's number of doctor visits in 2019 if he/she was in poor health, and did have insurance. e) The R² for this regression is

The Simple Linear Regression model is   Y = b0 + b1*X1 + u   and the Multiple Linear Regression model with k variables is:   Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u   Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term,   Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 16 In a t-test, suppose a researcher sets the significance level at 0.5%. What does this mean?    The probability that the null hypothesis is true is 0.5% The researcher would be rejecting the null hypothesis, only if the p-value is less than 0.5% The researcher would be rejecting the null hypothesis, if the t-statistic is higher than 0.5 It does not mean anything, because the significance level can only be set at 5%     QUESTION 17 In an MLR…

Find the least squares regression line for the data points. (Let x be the independent variable and y be the dependent varia (-1, 1), (1, -1), (3,-2) 2 X

Compute the sum-of-squares error (SSE) by hand for the given set of data and linear model. (7, 7), (8, 8), (9, 10); SSE = y = x - 1

Find the quadratic regression curve through the following points (2, 5), (3, 5), (5, 3) y = 3.0000x? 0.3333x + 1.6667 y = 3.0000x2 + 1.6667x – 0.3333 O y = -0.3333x2 + 1.6667x + 3.0000 O y = 1.6667x2 – 0.3333x + 3.0000

The Simple Linear Regression model is       Y = b0 + b1*X1 + u       and the Multiple Linear Regression model with k variables is:       Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u       Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term,       Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 7 In the MLR model, the assumption of ‘linearity in parameters’ is violated if:   one of the slope coefficients appears as a power (e.g. Y = b0 + b1*(X1^b2) + b3*X2 + u) the model includes the reciprocal of a variable (e.g. 1/X1) the model includes a variable squared (e.g. X1^2) the model includes a variable in its logarithmic form (i.e. log(X1) )     QUESTION 8 In the MLR model, the assumption of 'no perfect collinearity'…