A real estate agent wants to know whether both the internal square footage of a house and the external square footage of the house (i.e., the square footage of the land which does not contain the house itself) independently increase the sales price of the house.Data are collected from a random sample of recently-sold homes, and the sale price, internal square footage, and external square footage are recorded.The data are contained in a worksheet named "Houses" in the "Final Examination 2021.xlsx" file.Based on these data:

1. What is predicted sales price of a house which has 1,500 square feet of interior space and 500 square feet of exterior space (accurate to the nearest dollar)?
2. What is your best estimate of the proportion of the variation in sales price that is predicted in the population when both variables are in the model?
3. What is the value of the coefficient of partial determination for interior square footage (accurate to two places to the right of the decimal point), and what is the interpretation of this value?
4. In the context of the agent's objective, what is the interpretation of the intercept?
5. In the context of the agent's objective, what is the interpretation of the slope coefficient associated with interior square footage?
6. Can you be 95% confident that, after controlling for external square footage, higher internal square footage is associated with higher sales prices in the population?Justify your answer
7. In the context of the agent's objective, what can you infer from the p-value associated with the Global F?

Interior SF1,5971,3541,6231,2741,7891,5441,3111,1761,5121,2101,9671,5191,3761,5151,3791,5411,1991,7551,4321,8541,6191,1751,5901,2961,2721,4131,3921,4411,5541,4091,3771,5121,5911,4041,4961,7101,6701,4771,6231,5231,6181,5021,8831,6451,8601,6409761,3731,422

Exterior SF667, 541,673,398,676,847,549,482,609,643,664,561,726,756,456,612,457,640,561,722,561,512,639,673,456,640,577,709,630,519,457,588,673,460,755,630,707,573,537,564,537,734,610,606,755,683,512,500,492

Price$574,532$548,347$547,645$562,410$700,472$820,238$613,707$573,027$683,590$649,883$831,774$582,545$698,385$479,770$560,912$589,246$418,522$744,768$661,616$798,405$645,936$624,756$639,427$426,297$501,829$650,628$544,671$535,145$548,814$541,797$597,983$549,184$736,916$384,603$607,290$533,153$657,136$538,882$636,610$643,092$447,717$745,808$642,318$653,855$653,005$579,304$594,487$572,955$419,730