Question

A real estate developer is interested in determining the relationship between family income (X) and the
square footage of their home (Y). Seven families are randomly selected and the (X, Y) measurements are
as follows:

X ($1000) 22, 26, 45, 37, 28, 50, 56
Y (Sq Ft) 16, 17, 26 ,24, 22 ,21, 32

? = 37.71, ? = 22.57
Sxx = 1017.43, Sxy = 351.14, Sxyy = 179.71

(a) Sketch a scatter plot and determine whether it is acceptable to fit the data with a linear equation.
(b) Find the fitted regression equation.
(c) State the response and predictor variables.
(d) Are there any outliers or influential observations?
(e) Calculate SST, SSR, and SSE.
(f) Find and interpret the coefficient of determination, ?!.
(g) Find and interpret the correlation coefficient, ?.
(h) Predict y when x = 50.
(i) Predict y when x = 23.

Answer 1

b) Regression equation

y= 1.95*x-6.39

c) Response variable is square footage of their home and predictor variable is family income.

d) No outliers

e) SST= 1017.43

SSR= 686.10

SSE=331.33

f) coefficient of determination= 0.6743

Interpretation: the model explains 67.43% of the variability of the response data around its mean

g) r= sqrt(0.6743)= 0.8212

Positive correlation between these two variables.

h) x=50

y= 1.95*x-6.39

y= 1.95*50-6.39

y= 91.11

i) x= 23

y= 1.95*x-6.39

y=1.95*23-6.39

y=38.46