Question

DO NOT ANSWER IF YOU ARE UNSKILLED IN THIS AREA! THE DATA CHART IS CORRECT & COMPLETE!

Exercise 14-9 Algo

A realtor studies the relationship between the size of a house (in square feet) and the property taxes (in $) owed by the owner. The table below shows a portion of the data for 20 homes in a suburb 60 miles outside of New York City. [You may find it useful to reference the t table.]

Property Taxes	Size
21870	2467
17456	2493
18105	1876
15685	1055
43905	5603
33687	2518
15266	2257
16800	1989
18274	2025
16798	1343
15181	1371
36065	3003
31060	2816
42186	3362
14359	1544
38917	4064
25393	4083
22953	2469
16184	3587
29268	2860

Property Taxes			Size
	21,870			2,467
	17,456			2,493
	29,268			2,493

a-1. Calculate the sample correlation coefficient r_xy. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

Sample correlation coefficient

a-2. Interpret r_xy.

• The correlation coefficient indicates a positive linear relationship.

• The correlation coefficient indicates a negative linear relationship.

• The correlation coefficient indicates no linear relationship.

c-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Test statistic

Answer 1

Solutiona1:

Install analysis tool pak

in excel go to

data >data analysis >correlation

	Property Taxes(x)	Size(y)
Property Taxes(x)	1
Size(y)	0.748717	1

correlation coefficient=r=0.7487

SolutionA2:

there exists a strong positive relationship between property taxes and size

SolutionA3:

t=0.7487*sqrt(20-2)/sqrt(1-(0.7487^2))

t=4.792

ALTERNATIVELY YOU CAN ALSO DO IN R

cor.test(ds1$`Property Taxes(x)`,ds1$`Size(y)`)

OUTPUT:

earson's product-moment correlation

data: x and y
t = 4.7919, df = 18, p-value = 0.0001459
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.4579127 0.8947774
sample estimates:
cor
0.7487166

FROM THIS R OUTPUT:

correlation coefficient=0.7487

t=4.792