Question

12.	Below is a table detailing the number of days of personal travel over a year paired with annual household income (in 1000's of dollars) for 9 various families.
		HH Income ($000's)	Travel Days
		61	11
		32	6
		45	13
		35	9
		22	3
		89	21
		30	8
		74	15
		37	9
	a.	Construct a scatterplot for this data set in the region to the right (with household income as the independent variable, and travel days as the dependent variable.)
	b.	Based on the scatterplot, does it look like a linear regression model is appropriate for this data?  Why or why not?
	c.	Add the line of best fit (trend line/linear regression line) to your scatterplot. Give the equation of the trend line below.  Then, give the slope value of the line and explain its meaning to this context.
	d.	Determine the value of the correlation coefficient.  Explain what this value tells you about the two variables?
	e.	Based on the linear regression equation, what is the predicted number of personal travel days a person will take annually if their household income is $85,000?  Show your calculation.

Answer 1

a.

b. As we see that it is increasing trend and also if we draw a line through points, we see many points will fall on it, so linear model is appropriate

c.

Sum of X = 425
Sum of Y = 95
Mean X = 47.2222
Mean Y = 10.5556
Sum of squares (SS_X) = 4075.5556
Sum of products (SP) = 894.8889

Regression Equation = ŷ = bX + a

b = SP/SS_X = 894.89/4075.56 = 0.2196

For every increase in x, there is corresponding 0.2196 change in y.

a = M_Y - bM_X = 10.56 - (0.22*47.22) = 0.1868

ŷ = 0.2196X + 0.1868

d.

X Values
∑ = 425
Mean = 47.222
∑(X - M_x)² = SS_x = 4075.556

Y Values
∑ = 95
Mean = 10.556
∑(Y - M_y)² = SS_y = 224.222

X and Y Combined
N = 9
∑(X - M_x)(Y - M_y) = 894.889

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

r = 894.889 / √((4075.556)(224.222)) = 0.9361

e. For x=85 y=(0.2196*85)+0.1868=18.8528