Question

The dataset HomesForSaleCA contains a random sample of 30 houses for sale in California. Suppose that we are interested in predicting the Size (in thousands of square feet) for such homes.

State   Price   Size    Beds    Baths
CA      500     3.2     5       3.5
CA      995     3.7     4       3.5
CA      609     2.2     4       3
CA      1199    2.8     3       2.5
CA      949     1.4     3       2
CA      415     1.7     3       2.5
CA      895     2.1     3       2
CA      775     1.6     3       3
CA      109     0.6     1       1
CA      5900    4.8     4       4.5
CA      219     1.1     3       2
CA      255     1.2     3       2
CA      86      0.6     1       1
CA      62      1.2     3       2
CA      165     1.9     5       3.5
CA      1695    6.9     5       5.5
CA      499     1.4     3       2
CA      47      1.5     3       2
CA      195     2       3       2.5
CA      775     1       2       2
CA      199     1.4     3       2
CA      480     3       5       3
CA      173     0.9     3       1
CA      189     2.5     2       2
CA      230     1.7     3       2
CA      380     2.1     5       3
CA      110     0.8     2       1
CA      499     1.3     3       2
CA      399     1.4     3       2
CA      2450    5       4       5

1. What is the total variability in the sizes of the 30 homes in this sample? (Hint: Try a regression ANOVA with any of the other variables as a predictor.)

2. What other variable in the HomesForSaleCA dataset explains the greatest amount of the total variability in home sizes? Explain how you decide on the variable.

3. How much of the total variability in home sizes is explained by the "best" variable identified in question 2? Give the answer both as a raw number and as a percentage.

4. Which of the variables in the dataset is the weakest predictor of home sizes? How much of the variability does it explain?

5. Is the weakest predictor identified in question 4 still an effective predictor of home sizes? Include some justification for your answer.

thank you for your help!

Answer 1

Solution :

The regression with Price is:

	r²	0.430
	r	0.656
	Std. Error	1.096
	n	30
	k	1
	Dep. Var.	Size
ANOVA table
Source	SS	df	MS	F	p-value
Regression	25.36173499	1	25.36173499	21.10	.0001
Residual	33.65826501	28	1.20208089
Total	59.02000000	29
Regression output				confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	1.4987
Price	0.0008	0.00018305	4.593	.0001	0.0005	0.0012

The regression with Beds is:

	r²	0.412
	r	0.642
	Std. Error	1.113
	n	30
	k	1
	Dep. Var.	Size
ANOVA table
Source	SS	df	MS	F	p-value
Regression	24.3432	1	24.3432	19.66	.0001
Residual	34.6768	28	1.2385
Total	59.0200	29
Regression output				confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	-0.6617
Beds	0.8541	0.1927	4.434	.0001	0.4595	1.2488

The regression with Baths is:

	r²	0.846
	r	0.920
	Std. Error	0.570
	n	30
	k	1
	Dep. Var.	Size
ANOVA table
Source	SS	df	MS	F	p-value
Regression	49.9270	1	49.9270	153.74	6.86E-13
Residual	9.0930	28	0.3247
Total	59.0200	29
Regression output				confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	-0.8648
Baths	1.1859	0.0956	12.399	6.86E-13	0.9900	1.3818

(1) Total variability = 59.0200

(2) Baths explain the highest variability in Size (84.6%)

(3) 84.6%

(4) Beds is the weakest predictor. It explains 41.2% of the variability.

(5) Yes, it is effective since it's p-value is significant and there is a linear relationship of Beds with Size.

Please give me a thumbs-up if this helps you out. Thank you!