Let's consider the data from Airbnb in Chicago. We collected the price per night with number of bedrooms and the number of beds from randomly selected 40 listing properties:

(You can use Excel for this)

ID	bedrooms	beds	Price Per Night
1	3	3	190
2	2	2	89
3	2	2	501
4	1	1	104
5	2	4	399
6	1	1	42
7	1	4	108
8	5	6	170
9	1	1	132
10	3	1	48
11	2	6	99
12	3	3	192
13	3	3	502
14	1	2	91
15	1	1	99
16	0	1	76
17	4	4	182
18	4	5	131
19	1	1	98
20	3	5	247
21	0	1	85
22	1	1	151
23	0	2	116
24	1	2	42
25	0	2	202
26	1	2	60
27	4	7	298
28	2	8	116
29	3	3	94
30	1	2	52
31	2	2	61
32	1	1	90
33	2	2	83
34	1	0	130
35	1	2	132
36	1	2	209
37	4	4	252
38	2	2	247
39	3	3	199
40	2	3	185

bedrooms = the number of bedrooms at the property

beds = the number of beds at the property

Price Per Night = the dollar amount charged per night

Regression Analysis

Let's consider the following regression model. Estimate the model using Minitab and answer the questions using the output.

PricePerNight_i = b₀ + b₁ * bedrooms_i + e_t

Write the equationsfor the following statistics,find or calculate them from the output, and explain the meanings of the statistics (2 points each)

1) Estimated intercept and estimated slope coefficient

2) SST (Total Sum of Square), SSR (Regression Sum of Square), and SSE (Error Sum of Square)

3) R² (Coefficient of Determination) and r (correlation coefficient)

4) Standard Error of b1 and variance of b1

5) t test for the coefficient of income (Ho:b₁ = 0 )

6) F statistics and perform the test for the model

7) Standard deviation and variance of e_t

8) According to the model what are the predicted price per night and their confidence intervals if property has 0, 1, 2, 3, or 4 rooms?

9) List and explain the assumptions you made for a simple regression model.

10) Plot the residuals, and explain if you find any possible violations of assumptions on the regression model.