3. A sample of seven households was obtained, and information on their income and food expenditures for the past month was collected. The data (in hundreds of dollars) are: ) Put the points into...

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3. A sample of seven households was obtained, and information on their income and food expenditures for the past month was co

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Answer 1

Answer #1

Solution:

Given that the following information

A sample of seven households was obtained, and information on their income and food expenditure for the past month was collected.

a X Values 2200 3200 1600 3700 1200 2700 1700 Y Values 700 800 500 1000 400 600 600 .

b. (x- M)2 128.571 871.429 -728.571 1371.429 -1128.571 371.429 628.571 42.857 142.857 -157.143 342.857 -257.143 -57.143 -57.143

a.X Values
∑ = 16300
Mean = 2328.571
∑(X - M_x)² = SS_x = 4994285.714

Y Values
∑ = 4600
Mean = 657.143
∑(Y - M_y)² = SS_y = 237142.857

X and Y Combined
N = 7
∑(X - M_x)(Y - M_y) = 1008571.429

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 1008571.429 / √((4994285.714)(237142.857)) = 0.9268

Hence there is strong positive correlation

b. (Х-Мх)2 X- Mx (Х-М-ху. -128.5714 871.4286 -728.5714 1371.4286 -1128.5714 371.4286 -628.5714 42.8571 142.8571 -157.1429 342.85

Sum of X = 16300
Sum of Y = 4600
Mean X = 2328.5714
Mean Y = 657.1429
Sum of squares (SS_X) = 4994285.7143
Sum of products (SP) = 1008571.4286

Regression Equation = ŷ = bX + a

b = SP/SS_X = 1008571.43/4994285.71 = 0.2020

a = M_Y - bM_X = 657.14 - (0.2*2328.57) = 186.8993

ŷ = 0.2020X + 186.8993

c. For every increase in x, y will change to 0.2020 and this is value of slope

d. For x=5200,

ŷ = (0.2020*5200) + 186.8993=1237.2993

e. 1100 900- a 700 500- 300 ד 1000 1700 2400 3100 3800 x-Independent

x Values

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3. A sample of seven households was obtained, and information on their income and food expenditures for the past month was collected. The data (in hundreds of dollars) are: ) Put the points into...

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3. A sample of seven households was obtained, and information on their income and food expenditures for the past month was collected. The data (in hundreds of dollars) are: ) Put the points into...

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Add Answer to: 3. A sample of seven households was obtained, and information on their income and food expenditures for the past month was collected. The data (in hundreds of dollars) are: ) Put the points into...

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4. The following table presents data on x- the number of oil changes per year and y the cost of repairs for a sample of 10 cars from a given region: Number of oil changes per year (x ost of Repai...

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Add Answer to:
3. A sample of seven households was obtained, and information on their income and food expenditures for the past month was collected. The data (in hundreds of dollars) are: ) Put the points into...