Chapter 12 – problems Answers
1. a. There seems to be moderate positive trend.
b. r = 0.709,
c. The value of r indicates a moderate linear correlation..
d. Slope: For each increase of $1 in the 30-day advance fare, we would predict an
increase of $7.07 in the 1-day advance fare.
Y-intercept: If the price of the 30-day advance fare was $0, we would predict the
Price of the 1-day advance fare to be -$1237.60. (Clearly not practical.)
e. the residual for x = 260:
f. r2=0.502 = 50.2% 50.2% of the variation in the one day advance fare is explained by the variation in the 30-day advance fare.
g. Ho: ρ = 0
Ha: ρ ≠ 0
P-value =0.0745, Since p-value > α = 0.05, we conclude that at the 0.05 level of
Significance there is no significant linear correlation between the 30-day advance fare and the 1- day advance fare.
h. Since there is no linear correlation, we should not use the regression line to make a
prediction. We would predict the mean of the y-values or $690.
2. a. There is a positive trend. It appears fairly strong.
b. r = 0.901
c. r is quite close to 1, so there appears to be a strong linear relationship between the
number of commuters and the number of parking spaces.
d. Slope: For each increase of one commuter we would predict and increase of 0.41
parking spaces.
Y-intercept: At a station with 0 commuters we would predict 89.4 parking spaces.
e. Residual for x = 2641.
f. r2 = 0.812 = 81.2%
Approx. 81.2% of the variation in the number of parking spaces is explained by the variation in the number of commuters.
g. . Ho: ρ = 0
Ha: ρ ≠ 0
p-value = 0.0022, since the p-value < α = 0.05, we reject Ho and conclude that there
is significant linear correlation between the number of commuters and the number of
parking spaces.
h. x = 2000: Use the regression equation and predict 909.4 parking spaces.
x = 100,000 This number is well out of range of the given x-values, so using the
regression equation does not make sense. In this case predict the mean of the
y-values or 861.125 parking spaces.
i. For x = 2000,
the 95% interval is = .
For x = 2000 commuters we are 95% confident that the number of parking spaces
Will be between 398.2 and 1420.6.
3. a. There appears to be a fairly strong negative trend.
b. r = -0.944
c. r is quite close to -1, so there appears to be a fairly strong negative relationship
d. slope: For each increase of 1 pound in weight, we predict that the gas mileage will
decrease by 0.00797 mpg.
y-intercept: If a car weighs 0 pounds, the gas mileage would be 54.7 mpg. (not
practical.)
e. Residual for x = 3450
f. r2 = 0.891=89.1%
89.1% of the variation in the mpg is explained by the variation in weight of the car.
g. x=2700, since there is linear correlation and this value is within range, we use the regression line to predict a value.
mpg.
h. the 95% interval is =
We are 95% confident that the gas mileage for a car that weighs 2700 pounds would
Be between 36.98 miles per gallon and 29.38 miles per gallon.