1. (Chapter 3, pp. 65-67) Consider the multiple linear regression model y = ßo + ß1x1 + ẞ2x2 + ẞ3x3 + ß4x4 + ɛ. For the general linear hypothesis approach, find the appropriate D and d. (a) Hoẞ1+2ẞ2 = 3 B1 + B2 (b) Ho: = ß3 2 (c) Ho B1 B2, B3 = ß4 = (d) Ho B12ẞ2 = 4ẞ3, ẞ1 + 2ẞ2 = 0 : - (e) Ho : = B1 B2 = ß3 = ẞ4

A property agent wants to study the relationship between the age of a house (X) and its selling price (Y). Listed below is a random sample of houses that the agent has sold recently. [House]   [Age in Years (X)]   [Selling Price in $'m (Y)]     1                    9                                 2.2     2                    7                                 1.9     3                   11                                1.7     4                   12                                0.8     5                    8                                 2.5 a) Determine the linear regression equation.  b) i. If the age of a house is 10 year-old, what is the selling price?  ii. If the age of a house is 20 year-old, what is the selling price?  c) i. Determine the correlation coefficient.  ii. Interpret the result.

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 13 In the MLR model, what do we mean by Heteroskedasticity?   That the error term depends on the values of the explanatory variables That all the explanatory variables have different variance That the variance of the error term is a function of the explanatory variables That the variance of the error term is constant     QUESTION 14 Suppose that in the model Y=b0+b1*X1+u, we add a variable that is correlated with both Y and X1. What will happen…

An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65° F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be ŷ = 85 + 16x. The software used to compute the least-squares regression line for the equation above says that  r2 = 0.98.  This suggests which of the following? 1. Gas used increases by square root of 0.98 = 0.99 cubic feet for each additional degree-day?  2. Although degree-days and gas used are correlated, degree-days do not predict gas used very accurately. 3. Prediction of gas used from degree-days will be quite accurate.