AP Statistics
1. The decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper “Feeding of Predaceous Fishes on Our-Migrating Juvenile
Salmonids in the John Day Reservoir, Columbia River” (Trans. Amer. Fisheries Soc. (1991): 405-420) gave the accompanying data on y = maximum size of salmonids consumed by northern squaw fish (the most abundant salmonid predator) and x = squawfish length, both in mm. Use the computer output to answer the questions.
LSRL: size = -89.09 + .73 length r = s = t =
.981
12.56
s r 2 = .963
b
= .04778
15.26
df = 9
Predictor
Constant
Length s = 12.56 R-sq = 96.3%
Analysis of Variance
Source
Coef
-89.09
0.72907
Regression
Error
Total
DF
1
9
10
Stdev
16.83
0.04778 t-ratio
-5.29
15.26
R-sq(adj) = 95.9%
SS MS F p
36736 36736 232.87 0.000
1420 158
38156 p
0.000
0.000 p-value = .000
Calculate a 95% confidence interval for the slope of the true regression line: (-.62, .84)
What is the maximum size for salmonids consumed by a squawfish whose length is 375 mm, and what is the residual corresponding to the observation (375,165)?
184.295 mm, -19.295
2) Below is the computer output for the appraised value (in thousands of dollars) and number of rooms for houses in East Meadow, New York. Answer the following questions.
LSRL: r = s = value = 74.8 + 19.718 rooms
.661
29.05
r 2 = s b
=
.438
2.631
Predictor
Constant rooms s = 29.05
Coef
74.80
19.718
R-sq = 43.8%
Stdev
19.04
2.631
R-sq(adj) = 43.0% t-ratio
3.93
7.49 t = 7.49
p-value = 0.000
Interpret the slope. df = 72
Analysis of Variance
Source DF
Regression
Error
Total
1
72
73
SS
47398
60775
108173
MS
47398
844
There is an approximate increase of $19,718 in appraised value for an increase in one room.
Interpret the coefficient of determination.
Approximately 43.8% of the variation in appraised value is explained by the LSRL.
Predict the appraised value of a house with 13 rooms. $330,900

3) The manager of a chain of package delivery stores would like to predict the weekly sales (in $1000) for individual stores based on the number of customers. Find or calculate the related values for a two-sided test about the slope 
LSRL: r = s = t = sales = 2.423 + .0087 rooms
.9549
0.5015
13.64 r 2 = s b
= df =
.912
.0006397
18
Predictor
Constant
Customer
Coef
2.4230
0.0087293 s = 0.5015
Analysis of Variance
Source
Regression
DF
1
Error
Total
18
19
SS
Stdev
0.4810
0.0006397
R-sq = 91.2% t-ratio
R-sq(adj) = 90.7% p
46.834 46.834 186.22 0.000
4.527 0.251
51.360
MS F p-value = 0.000
90% confidence interval = (.00759, .00981)
4) A real estate agent would like to predict the selling price of a single-family house by predicting the price (in
$1000) based on the square footage (in 100 ft 2 ). Find or calculate the following answers.
LSRL: price = 18.35 + 3.87 footage r = s = t =
.805
12.9965
4.887
r 2 = s b
= df =
.648
.7936
13
Predictor
Constant
Customer
Regression
Error
Total
Coef
18.3538
3.8785 s = 12.9965
Analysis of Variance
Source DF
1
13
14
Stdev
14.8077
0.7936
R-sq = 64.8%
SS
4034.4144
2195.8215
6230.2360 t-ratio
R-sq(adj) = 62.0%
MS
4034.4144
168.9093
F
23.885 p-value = .0003
Interpret the slope & correlation coefficient.
S: For an increase of 100 square feet, there is an approximate increase of $3870 in the price of a house.
R: There is a strong, positive, linear association between square footage & price of a house.