Question

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.

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 16530.612 759387.755 530816.327 1880816.327 1273673.469 137959.184 395102.041 5510.204 124489.796 114489.796 470204.082 290204.082 -21224.490 35918.367 1836.735 20408.163 24693.878 117551.020 66122.449 3265.306 3265.306 2328 . 571 My: 657.143Sum: 4994285.714 Sum: 237142.857 Sum: 1008571.429 :

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 342.8571 -257.1429 -57.1429 -57.1429 5510.2041 124489.7959 114489.7959 470204.0816 290204.0816 -21224.4898 35918.3673 16530.6122 759387.7551 530816. 3265 1880816.3265 1273673.4694 137959.1837 395102.0408 SS 4994285.7143 SP 1008571.4286

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