Elementary Statistics
12th Edition
ISBN: 9780321836960
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 10.3, Problem 32BSC
Large Data Sets. Exercises 29-32 use the same Appendix B data sets as Exercises 29-32 in Section 10-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted values following the prediction procedure summarized in Figure 10-5.
32. Earthquakes Refer to Data Set 16 in Appendix B and use the magnitudes and depths from the earthquakes. Find the best predicted depth of an earthquake with a magnitude of 1.50.
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Students have asked these similar questions
Number 25
Section 10.2
Question #9
The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value?
Chirps in 1 min
981
1023
1074
1101
1203
874
Temperature
(°F)
83
79.4
80.9
82.8
92.3
72.8
What is the regression equation?
y= ___________+ ___________x
(Round the x-coefficient to four decimal places as needed. Round the constant to two decimal places as needed.)
What is the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute?
The best predicted temperature when a bug is chirping at
3000 chirps per minute is _________°F.
(Round to one decimal place as needed.)
Section 10.2
Question #10
Find the regression equation, letting overhead width be the predictor (x) variable. Find the best predicted weight of a seal if the overhead width measured from a photograph is 1.7cm. Can the prediction be correct? What is wrong with predicting the weight in this case? Use a significance level of 0.05.
Overhead Width (cm)
7.4
7.3
9.3
7.7
8.8
8.4
Weight (kg)
135
161
238
146
212
203
View the critical values of the Pearson correlation coefficient r.
Critical values of the pearson correlation coefficient r
n
α=0.05
α=0.01
NOTE: To test H0: ρ=0 against H1: ρ≠0, reject H0 if the absolute value of r is greater than the critical value in the table.
4
0.950
0.990
5
0.878
0.959
6
0.811
0.917
7
0.754
0.875
8
0.707
0.834
9
0.666
0.798
10
0.632
0.765
11
0.602
0.735
12
0.576
0.708
13
0.553
0.684
14
0.532…
Chapter 10 Solutions
Elementary Statistics
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forward
- If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?arrow_forwardKidsFeet Regression Line y-Intercept The KidsFeet dataframe contains data collected on 39 fourth grade students in Ann Arbor, MI, in October 1997. Two of the measurements taken on the children were the length in centimeters, (length), and width in centimeters, (width), of their longest foot. This data could be used to answer the following Research Question: How is the width of a fourth-grade student's foot related to the length? Which of the following is the y-intercept of the regression line? ## ## Simple Linear Regression## ## Correlation coefficient r = 0.6411 ## ## Equation of Regression Line:## ## length = 9.817 + 1.658 * width ## ## Residual Standard Error: s = 1.025 ## R^2 (unadjusted): R^2 = 0.411 ( ) 1.0248 ( ) 1.6576 ( ) 22.8153 ( ) 0.411 ( ) 9.8172 ( )0.6411arrow_forward
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