Linear regression decision model

Question

Assignment:

Q1. If the team of appraisers want to use a simple linear regression decision model (one X, one Y) based on either X₁ or X₂, which one of these independent variables do you recommend they use? Why?

Q2. Estimate the parameters, and therefore the prediction equation, for

Y = b₀+ b₁X₁ + b₂X₂

For each additional areal foot , what is the change in heating cost?

Q3. Set up a binary variable (X₃) for furnace age in combination with the model from part b. How much (%), if any, additional variability in heating cost, Y, does furnace age help explain?

Q4. What is the "best" model recommendation you can offer the home appraisal team using any combination of the independent variables from parts a through c above. Write the specific model.

Suite	Heating Cost	X1, Outside Temp	X2, Footage	X3, Furnace Age
1	$     198	29	1900	>5yrs
2	$     355	8	2800	<5yrs
3	$     291	6	2500	>5yrs
4	$     230	22	2000	<5yrs
5	$     121	55	1300	>5yrs
6	$     250	36	2100	>5yrs
7	$     360	28	2400	<5yrs
8	$     164	36	2300	<5yrs
9	$       42	59	1300	<5yrs
10	$       90	64	1500	>5yrs
11	$     271	19	2300	>5yrs
12	$       96	57	1400	>5yrs
13	$     187	39	1900	<5yrs
14	$     235	25	2100	>5yrs
15	$     138	28	1800	<5yrs
16	$       71	53	1200	<5yrs
17	$     206	47	2000	>5yrs
18	$     398	20	2900	>5yrs
19	$     319	39	2600	<5yrs
20	$       72	60	1500	>5yrs

Provide complete and step by step solution for the question and show calculations and use formulas.