Question

1. Selling price in millions of shilling and size of homes Table
Price      Size                Price     Size             Price                 Size
(‘000)    (sq. ft.)           (‘000)       (sq. ft.)      (‘000)               (sq. ft.)
268           1897              142             1329         83               1378
131           1157              107             1040         125             1668
112           1024              110              951           60              1248
112           935                187             1628          85              1229
122          1236               94               816            117            1308
128          1248               99               1060           57              892
158          1620               78                800          110             1981
135          1124               56                492          127             1098
146          1248               70                792          119             1858
126          1139               54                980          172              2010
(a) Plot the selling price versus the number of square feet. Describe the pattern. Does r 2
suggest that size is quite helpful for predicting selling price?
(b) Do a linear regression analysis. Give the least-squares line and the results of the
significance test for the slope. What does your test tell you about the relationship between size
and selling price?

1.b Do larger houses have higher prices? We expect that there is a positive correlation
between the sizes of houses in the same market and their selling prices. DATADATA

1.c DATA FILE HOUSESIZE
(a) Use the data in the Selling price and size of homes Table to test this hypothesis. (State
hypotheses, find the sample correlation r and the t statistic based on it, and give an approximate
P-value and your conclusion.)
(b) To what extent do you think that these results would apply to other cities in the United
States?

1.d Influence? Your scatterplot in Exercise shows one house whose selling price is quite high
for its size. Rerun the analysis without this outlier. Does this one house influence r 2, the
location of the least-squares line, or the t statistic for the slope in a way that would change your
conclusions?

Answer 1

The scatter plot is:

Price y = 0.077 x + 21.398 R2 = 0.431 500 1000 1500 2000 2500 Size

The least-squares line is:

y = 0.077 x + 21.398

For every additional sq. ft., price will increase by 0.077.

The hypothesis being tested is:

H0: β1 = 0

H1: β1 ≠ 0

The p-value from the output is 0.0001.

Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

	r²	0.431
	r	0.656
	Std. Error	33.845
	n	30
	k	1
	Dep. Var.	Price
ANOVA table
Source	SS	df	MS	F	p-value
Regression	24,250.8032	1	24,250.8032	21.17	.0001
Residual	32,073.8635	28	1,145.4951
Total	56,324.6667	29
Regression output				confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	21.3984
Size	0.0766	0.0166	4.601	.0001	0.0425	0.1107