Hi there!

I have solved all the answers below I just need help with the explanations of the meaning of the statistics.

Simple Regression analysis on Airbnb:

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. (excel file is available in D2L) :

ID	bedrooms	beds	PricePerNight
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

PricePerNight = 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 themfrom the output, and explainthe meanings of the statistics (2 points each)

1) Estimated intercept and estimated slope coefficient

Intercept is 97.54

Coefficient = 32.03

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

SST = 475513.6

SSR = 64000.06413

SSE = 411513.5359

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

R Square = 0.134591448

R = 0.3668670713

4) Standard Error of b1 and variance of b1

Standard Error of b1 = 13.17634583

Variance for b1 = 13.17634583² = 173.616

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

T stat = 2.431

6) F statistics and perform the test for the model

Null hypothesis Ho : b1 = 0.

Alternate hypothesis Ha : b1 not equal to 0.

F stat = 5.91

P-value = 0.0199

Since, the obtained P-value is less than 0.05, we reject the null hypothesis Ho.

There is sufficient evidence to conclude that coefficient slope is not equal to 0 and our regression model is significant.

7) Standard deviation and variance of e_t

MS for residual is Variance of et = 10829.30358

Standard deviation = 10829.30358 = 104.0639398639

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?

Given equation:

Y = 97.5399 + (32.0322*X).

For X = 0,

Y = 97.5399+(32.0322*0) = 97.54

For X = 1,

Y = 97.5399+(32.0322*1) = 129.572

For X = 2,

Y = 97.5399+(32.0322*2) = 161.604

For X = 3,

Y = 97.5399+(32.0322*3) = 193.636

For X = 4,

Y = 97.5399+(32.0322*4) = 225.669

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

There are four assumptions associated with a simple regression model:

• 1) Linearity: The relationship between X and the mean of Y is linear.
• 2) Homoscedasticity: The variance of residual is the same for any value of X.
• 3) Independence: Observations are independent of each other.
• 4) Normality: For any fixed value of X, Y is normally distributed.

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

bedrooms Residual Plot 400 200 Residuals 6 -200 bedroomsRESIDUAL OUTPUT Observation Predicted Price Per Night Residuals 193.6360721 -3.63607214 2 161.604008 -72.604008 3 161.604008 339.395992 4 129.5719439 -25.5719439 5 161.604008 237.395992 6 129.5719439 -87.5719439 7 129.5719439 -21.5719439 8 257.7002004 -87.7002004 9 129.5719439 2.428056112 10 193.6360721 -145.636072 11 161.604008 -62.604008 12 193.6360721 -1.63607214 13 193.6360721 308.3639279 14 129.5719439 -38.5719439 15 129.5719439 -30.5719439 16 97.53987976 -21.5398798 17 225.6681363 -43.6681363 18 225.6681363 -94.6681363 19 129.5719439 -31.5719439 20 193.6360721 53.36392786 21 97.53987976 -12.5398798 22 129.5719439 21.42805611 23 97.53987976 18.46012024 24 129.5719439 -87.5719439 25 97.53987976 104.4601202 26 129.5719439 -69.5719439 27 225.6681363 72.33186373 28 161.604008 -45.604008 29 193.6360721 -99.6360721 30 129.5719439 -77.5719439 31 161.604008 -100.604008 32 129.5719439 -39.5719439 33 161.604008 -78.604008 34 129.5719439 0.428056112 35 129.5719439 2.428056112 36 129.5719439 79.42805611 37 225.6681363 26.33186373 38 161.604008 85.39599198 39 193.6360721 5.363927856 40 161.604008 23.39599198