An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
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Compute the forecasted values for Yt for July and August in 2020 by using the modelsstated in (c) and (d)
For some genetic mutations, it is thought that the frequency of the mutant gene in men increases linearly with age. If m1 is the frequency at age t1, and m2 is the frequency at age t2, then the yearly rate of increase is estimated by r = (m2 − m1)/(t2 − t1). In a polymerase chain reaction assay, the frequency in 20-year-old men was estimated to be 17.7 ± 1.7 per μgDNA, and the frequency in 40-year-old men was estimated to be 35.9 ± 5.8 per μg DNA. Assume that age is measured with negligible uncertainty.a) Estimate the yearly rate of increase, and find the uncertainty in the estimate.b) Find the relative uncertainty in the estimated rate of increase.
The accompanying data file contains 40 observations on the response variable y along with the predictor variables x1 and x2. Use the holdout method to compare the predictability of the linear model with the exponential model using the first 30 observations for training and the remaining 10 observations for validation.
y
x1
x2
533.86
20
30
104.84
15
20
64.89
20
23
159.61
16
21
43.06
13
16
4.27
13
13
736.56
15
30
64.89
20
23
10.64
20
22
76.90
18
20
4.89
11
13
80.90
11
16
224.17
12
19
45.75
16
25
8.13
17
17
319.97
13
30
48.61
19
25
564.67
12
27
111.87
11
25
152.39
13
24
13.34
18
14
28.80
15
22
37.56
13
15
105.62
17
26
44.05
18
21
451.65
17
28
10.34
18
21
32.70
12
13
19.21
14
12
14.02
15
16
2.45
16
12
2.48
20
15
50.34
17
21
29.31
17
20
33.75
16
12
196.28
17
29
943.12
13
30
7.25
10
12
89.73
15
25
32.91
12
18
1. Use the training set to estimate Models 1 and 2.
Note: Negative values should be indicated by a…
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An Introduction to Statistical Methods and Data Analysis
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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_forwardDyslexia refers to a specific reading disability that affects 10% to 15% of the general population. A dyslexic child is defined as a child of normal or above-normal intelligence with no known organic behavioural disorders who, despite normal schooling, shows a reading lag of at least two years. A researcher proposed that dyslexia was the result of a complex visual deficit that could be immediately corrected by simply putting a blue plastic overlay on the reading material. To test this, 100 dyslexic children were randomly assigned to one of two groups, one of which read from pages with a clear plastic overlay and the other of which read from pages with a blue plastic overlay. The dependent variable was percentage correct on a multiple-choice reading comprehension test. a) Is this an observational study or an experiment? Explain your choice. b) Why did the researcher use a clear overlay as one of the treatment groups instead of just having the children read the passage without an…arrow_forwardDyslexia refers to a specific reading disability that affects 10% to 15% of the general population. A dyslexic child is defined as a child of normal or above-normal intelligence with no known organic behavioural disorders who, despite normal schooling, shows a reading lag of at least two years. A researcher proposed that dyslexia was the result of a complex visual deficit that could be immediately corrected by simply putting a blue plastic overlay on the reading material. To test this, 100 dyslexic children were randomly assigned to one of two groups, one of which read from pages with a clear plastic overlay and the other of which read from pages with a blue plastic overlay. The dependent variable was percentage correct on a multiple-choice reading comprehension test. What assumptions for the hypothesis test would need to be conducted for a one sample t test? Which data on spss would i need to look at for the assumptions?arrow_forward
- Second-Hand Smoke: Data Set 12 “Passive and Active Smoke” in Appendix B includes cotinine levels measured in a group of nonsmokers exposed to tobacco smoke (n = 40, Mean = 60.58 ng>mL, s = 138.08 ng>mL) and a group of nonsmokers not exposed to tobacco smoke (n = 40, Mean = 16.35 ng>mL, s = 62.53 ng>mL). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced. Use a 0.05 significance level to test the claim that nonsmokers exposed to tobacco smoke have a higher mean cotinine level than nonsmokers not exposed to tobacco smoke. Construct the confidence interval appropriate for the hypothesis test in part a. What do you conclude about the effects of second-hand smoke?arrow_forwardIf the general linear regression model is given by the equation: y = a + b?; considering the informationobtained in Figure 2 above, compute the value of a.arrow_forwardAt the 5% level of significance, which variables are statistically significant? If the price of cement per yard increases by 10, what will happen to the estimated quantity of cement demanded? What happens if it will increase by 20%?arrow_forward
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