The above SLR Model (1p) or (1s) is too simple to well explain the important birth weight variable, and people's economic condition as measured by family income should also be an important factor to consider. Hence Model (1p) is expanded as the following multiple linear regression (MLR) model: weight = &+ &ciga+ & inc+r, which is estimated based on the OLS method and the relevant data from BabyWeight as follows: weight = 117.1865 -0.5903 ciga +0.1220 inc + , (2p) (2s) (2.0326) (0.1207) (0.0512) [n=483, R = 0.0727, SSR = 187,375.7436] where inc is the average monthly family income of a surveyed woman in thousand dollars in the recent half-year, which for brevity is called monthly family income or just family income in this Assignment. Q2a (4 marks): Briefly explain why the (population & or its) sample estimate is negative, while the (population or its) sample estimate 2 is positive. Q2b (6 marks): Indicate two facts to briefly explain that the estimated MLR Model (2s) could be considered better than the estimated SLR Model (1s). Q2c (6 marks): Woman B (in Q1) had a monthly family income of $11,500. What is the estimated or expected birth weight (denoted as weight B2) of her new-born baby based on Model (2s)? Is weightB1 or weight 2, the estimated birth weight based on Model (1s) or Model (2s), closer to the real birth Win weight of Woman B's new-born baby, and why? Go to Settings to Q2d-even (8 marks) for students with even Student Numbers only: Woman D smoked the same amount of cigarettes per day during pregnancy as Woman B (in Q1), but her monthly family income was $20,000 higher than Woman B's. Find the difference in the estimated birth weights for Women B's and D's newly-born babies based on Model (2s). Can you test the significance of this difference at the 5% level? If yes, please formally perform the test. If no, please explain why. Q2e (10 marks): Woman A (in Q1) had a monthly family income of $31,500. Then what is the estimated birth weight (denoted as weight 42) of her new-born baby based on Model (2s)? Find the difference in the two estimated birth weights (weight A2 and weight32) for Women A's and B's new-born babies based on Model (2s), and briefly comment on the practical and statistical significance of this difference. Q2f (6 marks): Compared to Woman E, Woman F smoked 10 more cigarettes per day during pregnancy and her monthly family income was $20,000 lower. Find the estimated difference in the birth weights for their new-born babies based on Model (2s). Any comments in relation to Q2e's relevant result? Q2g (14 marks): As a knowledgeable AE student, in addition to the above SLR and MLR Models (1s) and (2s) [or Models (1p) and (2p)] for explaining new-born baby's birth weight in different ways, you are also interested in understanding the relationship between the two IVs, cigarettes smoked (ciga) and family income (inc). Hence you propose the following SLR model: (3p) inc ciga+u, and then estimate this model using the OLS method and the relevant data from BabyWeight as follows: inc= 0 + ciga+ . (3s) Can you find the values of the sample estimated 40 and based on the available information up to this point? If yes, please show your work and find them. If no, please explain why.