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Number of Households and Amount spent on groceries, Correlation

The number of household members (X) and the amount spent on groceries (in $) per week (Y) are measured for six households in a local area in New York City. The data are given in the table below.

XYX2Y2XY
290
3120
5175
4125
135
8220
Totalabcde

Complete the above table in a sheet of paper and answer the following:

Remark: Round your answers to 2 decimal places

The value of a is Blank 1

The value of b is Blank 2

The value of c is Blank 3

The value of d is Blank 4

The value of e is Blank 5

What is the value of SS(X)?

The answer: Blank 6

What is the value of SS(Y)? =

The answer: Blank 7

What is the value of SS(XY)?

The answer. Blank 8

What is the value of the coefficient of linear correlation (r)?

The answer: Blank 9

Solution

Blank 1 : 23

Blank 2: 765

Blank 3: 119

Blank 4: 118,375

Blank 5: 3,710

Blank 6: 30.83

Blank 7: 20,837.50

Blank 8: 777.50

Blank 9: 0.97

Calculations

XYX2Y2XY
29048100180
3120914400360
51752530625875
41251615625500
1351122535
822064484001760
Total237651191183753710
abcde

Key:

X: X Values
Y: Y Values
Mx: Mean of X Values
My: Mean of Y Values
X – Mx & Y – My: Deviation scores
(X – Mx)2 & (Y – My)2: Deviation Squared
(X – Mx)(Y – My): Product of Deviation Scores

X – MxY – M(X – Mx)2(Y – My)2 (X – Mx)(Y – My)
-1.83-37.5          3.361406.2568.8
-0.83-7.5          0.6956.256.3
1.1747.5          1.362256.2555.4
0.17-2.5          0.036.25-0.4
-2.83-92.5          8.038556.25262.1
4.1792.5        17.368556.25385.4
SS(X)SS(Y)SS(XY)
Mx: 3.83My: 127.50 Sum: 30.83Sum: 20837.50Sum: 777.50

X Values
∑ = 23
Mean = 3.833
∑(X – Mx)2 = SSx = 30.833

Y Values
∑ = 765
Mean = 127.5
∑(Y – My)2 = SSy = 20837.5

X and Y Combined
N = 6
∑(X – Mx)(Y – My) = 777.5

R Calculation
r = ∑((X – My)(Y – Mx)) / √((SSx)(SSy))

r (blank 9)= 777.5 / √((30.833)(20837.5)) = 0.97

The number of household members (X) and the amount spent on groceries (in $) per week (Y) are measured for six households in a local area in New York City. The data are given in the table below.
	X	Y	X2	Y2	XY
	2	90			
	3	120			
	5	175			
	4	125			
	1	35			
	8	220			
Total	a	b	c	d	e

By considering the value of the linear correlation coefficient (r) that you have calculated for the question “The number of household members (X) and the amount spent on groceries (in $) per week (Y) are measured for six households in a local area in New York City.”
The variables (X) and (Y) have a_

Answer:

High positive linear correlation

Explanation:

as r = 0.97

Which means the number of amount spent on groceries (in$) increase as the number of household members (X) increases.

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