Question

1.

A sample of customers in a grocery store were asked the amount they spent at the grocery store and the number of household members for whom they currently shopped. The results are summarized in the table below:

Number of Household Members (x)	Dollar Amount Spent on Groceries (y)
5	135
2	49
2	50
1	37
4	91
3	68
5	133
3	60

Find the correlation coefficient for the number of household members versus the dollar amount spent on groceries and round this result to the hundredths place.

		-0.53
		-0.23
		0.17
		0.47
		0.96

2.

Given a trendline of y = 5987x + 143960, where the variable x represents the age of a home (in years) and the variable y represents its current market value (in dollars), use this trendline to predict the current market value of an 8-year old home.  

		$191,856.00
		$1,151,680.00
		$53,883.00
		$1,157,667.00
		$1,199,576.00

Answer 1

Solution:

Question 1

The formula for correlation coefficient is given as below:

Correlation coefficient = r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

The calculation table is given as below:

No.	x	y	x^2	y^2	xy
1	5	135	25	18225	675
2	2	49	4	2401	98
3	2	50	4	2500	100
4	1	37	1	1369	37
5	4	91	16	8281	364
6	3	68	9	4624	204
7	5	133	25	17689	665
8	3	60	9	3600	180
Total	25	623	93	58689	2323

∑x = 25

∑y = 623

∑x^2 = 93

∑y^2 = 58689

∑xy = 2323

n = 8

r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

r = [8*2323 - 25*623]/sqrt[(8*93– (25)^2)*(8*58689 - (623)^2)]

r = 3009 / sqrt[(8*93– (25)^2)*(8*58689 - (623)^2)]

r = 3009 / sqrt[9684577]

r = 3009/ 3112.005

r = 0.966901

Correlation coefficient = r = 0.96

Question 2

We are given

y = 5987*x + 143960

We are given

x = 8

y = 5987*8 + 143960

y = 191856

Answer: $191,856.00