Question

Please help with test statistic and p value

A realty company would like to develop a regression model to help it set weekly rental rates for beach properties (y). The independent variables for this model are Use the accompanying data to complete () its age (X2)- the number of bedrooms a property has and the number of blocks away from the ocean it is (3) parts a through e below BE Click the icon to view the rental property data. a) Using technology, construct a regression model using all three independent variables. 9-(7022.2) ( 430.9) x, (25.9)-(-2307.6) X2 + (Round to one decimal place as needed.) b) Test the significance of each independent variable using a 0.10. Test the significance of x. Identify the nul and alternative hypotheses. Ho: P H,: B (Type integers or decimals.) Enter your answer in the edit fields and then click Check Answer. Check Answer parts remaining Clear All 17 hdep re (XiRental Property Data e the er Rental ($) Bedrooms Age Blocks ion 1000 2 17 3.5 1100 2 4 2 1700 2.5 4 6 ) 2300 4 2.5 14 der 3100 5 10 2.5 3200 ull A 14 2.5 3600 4 6 3 4800 5 7 1.5 6000 18 4 1.5 9100 6 7 1 Print Done d t Clear All $ & ( 4 5 6 8 99 LO

Answer 1

a) Using r software, we have constructed regression model using three independent variables.  

> D= read.csv("C:/Users/DELL/Desktop/Rental Property Data.csv",header = T)
> D

Rental	Bedrooms	Age	Blocks
1000	2	17	3.5
1100	2	4	3
1700	4	6	2.5
2300	4	14	2.5
3100	5	10	2.5
3200	4	14	2.5
3600	4	6	3
4800	5	7	1.5
6000	4	18	1.5
9100	6	7	1

> mod= lm(Rental~Bedrooms+Age+Blocks, data = D)
> mod

Call:
lm(formula = Rental ~ Bedrooms + Age + Blocks, data = D)

Coefficients:
(Intercept) Bedrooms Age Blocks
7022.21 430.87 25.94 -2307.61

> summary(mod)

Call:
lm(formula = Rental ~ Bedrooms + Age + Blocks, data = D)

Residuals:
Min 1Q Median 3Q Max
-1432.31 -921.62 -52.37 625.94 1621.50

Coefficients:

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	7022.21	4717.04	1.489	0.1871
Bedrooms	430.87	604.47	0.713	0.5027
Age	25.94	90.40	0.287	0.7838
Blocks	-2307.61	945.38	-2.441	0.0504

---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1326 on 6 degrees of freedom
Multiple R-squared: 0.8121,   Adjusted R-squared: 0.7182
F-statistic: 8.644 on 3 and 6 DF, p-value: 0.01345
hence we have the regression equation,

est, y = 7022.2 + 430.9 x₁ + 25.9 x₂  - 2307.6 x₃

b) H₀ : β₁ = β₂ = β₃ = 0

H1 : At least one β_j ≠ 0 (for j = 1, 2, 3)

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	3	45615168	15205056	8.64	0.013
Bedrooms	1	893715	893715	0.51	0.503
Age	1	144854	144854	0.08	0.784
Blocks	1	10480194	10480194	5.96	0.05
Error	6	10553832	1758972
Lack-of-Fit	5	10148832	2029766	5.01	0.326
Pure Error	1	405000	405000
Total	9	56169000

F = 8.64, P = 0.013 < 0.1

So here we reject H_0, hence we conclude that at least one of the slope parameters is not equal to 0.

Test of significance of x₁

H₀ : β₁ = 0

H1 : β₁ ≠ 0

P = 0.503 > 0.1 so here we accept H₀.

Hence we conclude that slope parameter is equal to 0.