# AP Release Question WorksheetChapter 5

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```					1. A least squares regression line was fitted to the weights (in pounds) versus age (in months) of a group of many
young children. The equation of the line is y  16.6  0.65t , where y is the predicted weight and t is the age of
the child. A 20-month old child in this group has an actual weight of 25 pounds. Which of the following is the
residual weight, in pounds, for this child?
a) -7.85        b) -4.60         c) 4.60         d) 5.00         e) 7.85

2.   There is a linear relationship between the number of chirps made by the striped ground cricket and the air
temperature. A least squares fit of some data collected by a biologist gives the model: y  25.2  3.3x for

9  x 25 , where x is the number of chirps per minute and y is the estimated temperature in degrees
Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per
minute?
a) 3.3 Fahrenheit b) 16.5 Fahrenheit c) 25.2 Fahrenheit d) 28.5 Fahrenheit e) 41.7 Fahrenheit

3.   The equation of the least squares regression line for the points a scatterplot is y  1.3  0.73x . What is the
residual for the point (4,7)?
a) 2.78          b) 3.00        c) 4.00        d) 4.22      e) 7.00

4.    Each of 25 adult women were asked to provide her own height (y), in inches, and the height (x), in inches of her
father. The scatterplot below displays the results. Only 22 of the 25 pairs are distinguishable because some of
the (x,y) pairs were the same. The equation of the least squares regression line is y  35.1  0.427 x .

b) One father’s height was x  67 inches and his
daughter’s height was y  61 inches. Circle the
point on the scatterplot above that represents
this pair and draw the segment on the
scatterplot that corresponds to the residual for
it. Give a numerical value for the residual.

c) Suppose the point x  84, y  71is added to
the data set. Would the slope of the least
squares regression line increase, decrease, or
(Note: no calculations are necessary to answer
a) Draw the least squares regression line on the                       this question.)
scatterplot above.

5.    A real estate agent is interested in developing a model to estimate the prices of houses in a particular part of a
large city. She takes a random sample of 25 recent sales and, for each house, records the price (in thousands of
dollars), the size of the house (in square feet), and whether or not the house has a swimming pool. This
information, along with regression output for a linear model using size to predict price, is shown below
Price       Size            Pool   Residual                      Linear Fit: Price = -28.144 + 0.165size
(\$1,000s)   (Square feet)          (\$1,000s)
274         1,799           Yes    6                             Summary of Fit: RSquare = 0.722
330         1,875           Yes    49
307         2,145           Yes    -18
376         2,145           Yes    42
352         2,300           Yes    1
409         2,350           Yes    50
375         2,589           Yes    -23
498         2,943           Yes    42
248         1,600           No     13
265         1,623           No     26
228         1,829           No     -45
303         1,875           No     22
303         1,950           No     10
251         1,975           No     -46
244         2,000           No     -57
347         2,274           No     1
345         2,279           No     -2
282         2,300           No     -69
389         2,392           No     23
413         2,410           No     44
353         2,428           No     -19
419         2,560           No     26
348         2,639           No     -58
365         2,701           No     -52
474         2,849           No     33

a) Interpret the slope of the least square regression line in the context of the study.
b) The second house in the table has a residual of 49. Interpret this residual value in the context of the study.

The real estate agent is interested in investigating the effect of having a swimming pool on the price of a house.

c) Use the residuals from all 25 houses to estimate how much greater the price for a house with a swimming pool
would be, on average, than the price for a house of the same size without a swimming pool.

To further investigate the effect of having a swimming pool on the price of a house, the real estate agent creates two
regression models, one for houses with a swimming pool and one for houses without a swimming pool. Regression
output for these two models is shown below.

d) Use the regression model for houses with a swimming pool and the regression model for houses without a
swimming pool to estimate how much greater the price for a house with a swimming pool would be than the
price for a house of the same size without a swimming pool. How does this estimate compare with your result
from part c?

Linear Fit (pool = yes):
Price = -11.602 + 0.166size
Linear Fit (pool = no):
Price = -27.382 + 0.160size

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