1 answer

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

Question:

3. A sample of seven households was obtained, and information on their income and food expenditures for the past month was co
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 your calculator list. Use your calculator to perform linear regression. What is the correlation? Is it positive, negative, or neither? Is it strong or weak? Find the equation of the line of best fit. (c) Write a sentence that interprets the estimated slope. (d) Use your line of best fit to predict the food expense for a family with $5200. (e) Insert a picture of your calculator screen showing the scatter plot and line of best fit.

Answers

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.

aX 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 - Mx)2 = SSx = 4994285.714

Y Values
∑ = 4600
Mean = 657.143
∑(Y - My)2 = SSy = 237142.857

X and Y Combined
N = 7
∑(X - Mx)(Y - My) = 1008571.429

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

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 (SSX) = 4994285.7143
Sum of products (SP) = 1008571.4286

Regression Equation = ŷ = bX + a

b = SP/SSX = 1008571.43/4994285.71 = 0.2020

a = MY - bMX = 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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