Question

Use the following information for questions 1-5.

Do larger families spend more per week on food? A sample of 10 families in Chicago revealed the following data for family size and the weekly grocery bill. (Part of the calculations are done for you.)

           Family size     $Groceries     (X-Xbar)        (Y-Ybar)       (X-Xbar) x (Y-Ybar)

•          3                 99                -1                 -11                        11
•          6                114                2                    4                          8
•          5                131                1                   21                       21
•          6                129                2                   19                       38
•          6                142                2                   32                       64
•          3                111               -1                    1                       
•          4                104                0
•          2                  81
•          2                  98
•          3                  91
•         40             1100

Sx = 1.63     Sy = 19.28     X-bar = 40/10 = 4    Y-bar = 1100/10 = 110

Grocery Question #1: Calculate ∑ (X - Xbar) x (Y - Ybar)

	A.	236
	B.	238
	C.	240
	D.	242

Grocery Question #2: Assuming that ∑ (X - Xbar) x (Y - Ybar) is equal to 242, calculate r.

	A.	+0.856
	B.	+0.858
	C.	+0.860
	D.	+0.862

Grocery Question #3: Assuming that r = +0.856, determine the regression equation,

		Y = 10.125 + 69.5X
		Y = 69.5 + 10.125X
		Y = 70 + .858X
		Y = 0.858 + 70X

Grocery Question #4: Assuming that the Regression equation is Y = 70 + .858X, how much would you expect a family of five to spend on groceries over a week's time?

	A.	$73
	B.	$74
	C.	$75
	D.	$76

Grocery Question #5: Assuming that the coefficient of determination is 0.732, what conclusion can you reach?

	A.	26.8% of the grocery bill can be explained by the variation in family size.
	B.	73.2% of the family size can be explained by the variation in the grocery bill.
	C.	73.2% of the weekly grocery bill can be explained by the variation in family size.
	D.	The coefficient of correlation is 0.536.

Answer 1

family size(x)	groceries(y)
3	99	-1	-11	11
6	114	2	4	8
5	131	1	21	21
6	129	2	19	38
6	142	2	32	64
3	111	-1	1	-1
4	104	0	-6	0
2	81	-2	-29	58
2	98	-2	-12	24
3	91	-1	-19	19
				sum= 242

given that,

, , ,

1)using the calculated table and given data:-

.

2) correlation coefficient (r) be:-

3). our regression slope and intercept be:-

so our regression equation be:-

Y = 69.5 + 10.125 X

4).Assuming that the Regression equation is Y = 70 + .858 X, i can expect a family of five to spend on groceries over a week's time is :-

dollars

5: Assuming that the coefficient of determination is 0.732, we can conclude that:-

73.2% of the weekly grocery bill can be explained by the variation in family size.

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