Elementary Statistics
12th Edition
ISBN: 9780321836960
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 10.3, Problem 26BSC
Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-2. In each case, find the regression equation, letting tire first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5.
25. Gas Prices One gas station not included in the table below had a listed price of $2.78 for regular gas. Find the best predicted price of premium gas at this station. Is the result close to the actual price of $2.93 for premium gas?
| Regular | 2.77 | 2.77 | 2.79 | 2.81 | 2.78 | 2.86 | 2.75 | 2.77 |
| Mid-Grade | 3 00 | 2.77 | 2.89 | 2.93 | 2.93 | 2.96 | 2.86 | 2.91 |
| Premium | 3.07 | 3.09 | 3.00 | 3.06 | 3.03 | 3.06 | 3.02 | 3.03 |
26. Gas Prices Using the data from the preceding exercise, find the best predicted price for mid-grade gas for a station that posted $2.78 as the price of regular gas. Is the result close to the actual price of $2.84 for mid-grade gas?
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Business discuss
Spam filters are built on principles similar to those used in logistic regression. We fit a probability that each message is spam or not spam. We have several variables for each email. Here are a few: to_multiple=1 if there are multiple recipients, winner=1 if the word 'winner' appears in the subject line, format=1 if the email is poorly formatted, re_subj=1 if "re" appears in the subject line. A logistic model was fit to a dataset with the following output:
Estimate
SE
Z
Pr(>|Z|)
(Intercept)
-0.8161
0.086
-9.4895
0
to_multiple
-2.5651
0.3052
-8.4047
0
winner
1.5801
0.3156
5.0067
0
format
-0.1528
0.1136
-1.3451
0.1786
re_subj
-2.8401
0.363
-7.824
0
(a) Write down the model using the coefficients from the model fit.log_odds(spam) = -0.8161 + -2.5651 + to_multiple + 1.5801 winner + -0.1528 format + -2.8401 re_subj(b) Suppose we have an observation where to_multiple=0, winner=1, format=0, and re_subj=0. What is the predicted probability that this message is spam?…
Consider an event X comprised of three outcomes whose probabilities are 9/18, 1/18,and 6/18.
Compute the probability of the complement of the event.
Question content area bottom
Part 1
A.1/2
B.2/18
C.16/18
D.16/3
Chapter 10 Solutions
Elementary Statistics
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