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Unformatted text preview: STAT 252  Exam 2
11.03.00 INSTRUCTIONS: Please start each problem on a new page in your blue book. Be neat and show
work for maximum credit. 1. The following data on illiteracy rate (y) and school enrollment rate (x) was collected for a random
sample of states in the US. Regression
Model Summary Std. Error
Adjusted of the
o R S uare Estimate
mmmml 3 Predictors: (Constant). X ANOVA" X
S  uares S uare F 
1 Regression 168.813 168.813 88.650
Residual 32.373 1.904
Total 201.185 8 Predictors: (Constant), X ssxx = 2049.6211
ssyy = 201.1352
ss,‘y = 588.2195 b  I J? = 66.0684
 Dependent Vanable. Y y = 5.7642
Coefﬁcientsa n = 19 Standardi
zed
Unstandardized Coefﬁcien
Coefﬁcients ts
I! a 1 (Constant) 6.01615“ 2.039 12.139 .000
x  ’1 .030 v : 601i .000
3 Dependent Variable: Y . a. (5) Find the regression equation.
b. (10) Find and interpret the correlation coefficent. c. (10) Does the data show that school enrollment is useful for predicting illiteracy rate? Test
using a = 0.01 d. (10) Calculate a 95% prediction interval for illiteracy rate when enrollment is 75 percent
(NOTE: don’t waste time interpreting) ' e. (5) Draw a happy face for 5 points ©. Keep going, you're doing a good job. 2. Data was collected for a random sample of hotels in California. The information obtained includes (y) daily rate (32), (x1) rating of the hotel (1 to 3 stars with 3 stars being the best), and (x2) number
of rooms in the hotel. Regression
Model Summary Std. Error
Adjusted of the
R Suare R Suare Estimate
) .33! 3 Predictors: (Constant , X1X2, X1, X2 ANOVA"
Sum of Mean
S uares df S  uare F Si  1 Regression 4613347 3 1537.982 22.769 .OtillJ‘i
Residual 2093.939 31 67.546
Total 6707.886 34 3 Predictors: (Constant), X1 X2, X1, X2
b Dependent Variable: Y Coefﬁcientsa Unstandardized
Coefﬁcients 8 Dependent Variable: Y a. (5) State the model used in the analysis. b. (10) Does the data provide evidence to suggest that the relationship between daily rate
and number of rooms depends on hotel rating? Test using a = 0.05 c. (10) Estimate and interpret the rate of change in daily rate for a one room increase for a
hotel with a 3 star rating. 3. Each of 36 men, while blindfolded, was asked to touch the foreheads of three women, one of
whom was their spouse. The two “decoy” women were the same age, height and weight as the
man's partner. Of the 36 men tested, 18 were able to correctly identify their spouse. Of course
one would expect 12 of the 36 men to be correct if they were all guessing. a. (15) Do the data provide sufﬁcient evidence to suggest that men will do differently, with
respect to being correct, than if they were guessing? Test using a: = 0.05. 4. Data were collected randomly with respect to three different variables: y, x1, and x2. Assuming the
model y = 130 + [3,x1 + ﬁle + g was fit. answer the following questions. a. (5) Identify (below) the appropriate ANOVA table for this analysis. ANOVA
Sum of ‘
Snares of Mean Suare F
1 Regression 76536472330 4 19134118082 . Residual
Total 60074292070
1 .3661 E+1 1 63236096916 ANOVA 1 Regression 750120356856 37506017843 Residual 615987287144 97 63503844035
Total 136610764400 99 ANOVA 1 Regression
Residual
Total 76501718347
601 09046053
136610764400 b. (10) Do the data show signs of multicollinearity? Justify and be speciﬁc.
CoefﬁcientsEl Standardi
zed Unstandardized Coefﬁcien
Coefﬁcients ts n (Constant) 38233.622 11414.054 1.952 .739 . .
1.155 . . . 3 Dependent Variable: Y \ c. (5) What seems like the most appropriate correlation coefﬁcent between x1 and x2? x7“ ...
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