Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337794503
Author: PECK
Publisher: Cengage
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Textbook Question
Chapter 5, Problem 85E
Suppose the hypothetical data below are from a toxicity study designed to measure the effectiveness of different doses of a pesticide on mosquitoes. The table below summarizes the concentration of the pesticide, the sample sizes, and the number of mosquitoes killed.
- a. Make a
scatterplot of the proportions of mosquitoes killed versus the pesticide concentration. - b. Using the techniques introduced in this section, calculate
- c. The point at which the dose kills 50% of the mosquitoes is sometimes called LD50, for “Lethal dose 50%.” What would you estimate LD50 to be for this pesticide when used on mosquitoes?
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Please help with part c. The first picture has all of the data.
We are interested in using the pH of the lake water (which is easy to measure) to predict the
average mercury level in fish from the lake, which is hard to measure. Let x be the pH of the
lake water and Y be the average mercury level in fish from the lake. A sample of n = 10 lakes
yielded the following data:
Observation (i)
pH (x;)
Average mercury level (y;)
1
3
6
7
9
10
8.2
8.4
7.0
7.2
7.3
6.4
9.1
5.8
7.6
8.1
0.15
0.04
0.40
0.50
0.27
0.81
0.04
0.83
0.05
0.19
Suppose we fit the data with the following regression model:
Y; = a+ Bx; + Ei, i = 1, ... ,
10,
where ɛ; ~ N(0, o²) are independent. We have the following quantities: a = E1 ; = 7.51,
j = £i=1 Yi =
0.328, E1 x? = 572.71, 1 y? = 1.8922, -1 Tiyi = 22.218.
n
i=1
Some R output that may help.
> p1 qt (p1, 8)
[1] -2.896 -2.306 -1.860 -1.397
> qt (p1, 9)
[1] -2.821 -2.262 -1.833 -1.383
1.397
1.860
2.306 2.896
1.383
1.833
2.262
2.821
(a) Find the ordinary least squares (OLS) estimates (denoted as â and B) of the regression
coefficients…
We are interested in using the pH of the lake water (which is easy to measure) to predict the
average mercury level in fish from the lake, which is hard to measure. Let x be the pH of the
lake water and Y be the average mercury level in fish from the lake. A sample of n = 10 lakes
yielded the following data:
Observation (i)
pH (x;)
Average mercury level (y;) 0.15
1
3
4
6
7
8
9
10
8.2
8.4
7.0
7.2
7.3
6.4
9.1
5.8
7.6
8.1
0.04
0.40
0.50
0.27
0.81
0.04
0.83
0.05
0.19
Suppose we fit the data with the following regression model:
Y; = a + Bx; + Ei, i = 1, ..., 10,
where ɛi ~
N (0, o?) are independent. We have the following quantities: a = E=1 ¤i = 7.51,
j = E1 Yi = 0.328, 1 x = 572.71, 1 Y? = 1.8922, D-1 *iYi = 22.218.
i=1
ri=1
Some R output that may help.
> р1 qt (p1, 8)
[1] -2.896 -2.306 -1.860 -1.397
1.397
1.860
2.306
2.896
> qt (p1, 9)
[1] -2.821 -2.262 -1.833 -1.383
1.383
1.833
2.262
2.821
(a) Find the ordinary least squares (OLS) estimates (denoted as â and ß) of the regression…
Chapter 5 Solutions
Introduction To Statistics And Data Analysis
Ch. 5.1 - For each of the scatterplots shown, answer the...Ch. 5.1 - For each of the following pairs of variables,...Ch. 5.1 - For each of the following pairs of variables,...Ch. 5.1 - For each of the following pairs of variables,...Ch. 5.1 - Is the following statement correct? Explain why or...Ch. 5.1 - Draw a scatterplot for which r = 1.Ch. 5.1 - Draw a scatterplot for which r = 1.Ch. 5.1 - Each year J.D. Power and Associates surveys new...Ch. 5.1 - The accompanying data are x = Cost (cents per...Ch. 5.1 - The authors of the paper Flat-footedness Is Not a...
Ch. 5.1 - The paper The Relationship Between Cell Phone Use,...Ch. 5.1 - Data from the U.S. Federal Reserve Board (federal...Ch. 5.1 - The article 115K! The 13 Best Paying U.S....Ch. 5.1 - It may seem odd, but one of the ways biologists...Ch. 5.1 - An auction house released a list of 25 recently...Ch. 5.1 - A sample of automobiles traversing a certain...Ch. 5.2 - Two scatterplots are shown below. Explain why it...Ch. 5.2 - The authors of the paper Statistical Methods for...Ch. 5.2 - The accompanying data are a subset of data from...Ch. 5.2 - The authors of the paper Evaluating Existing...Ch. 5.2 - The authors of the paper referenced in the...Ch. 5.2 - A sample of 548 ethnically diverse students from...Ch. 5.2 - The relationship between hospital patient-to-nurse...Ch. 5.2 - The report Airline Quality Rating 2016...Ch. 5.2 - Acrylamide is a chemical that is sometimes found...Ch. 5.2 - Use the acrylamide data given in the previous...Ch. 5.2 - Studies have shown that people who suffer sudden...Ch. 5.2 - The data given in the previous exercise on x =...Ch. 5.2 - An article on the cost of housing in Califomia...Ch. 5.2 - The following data on sale price, size, and...Ch. 5.2 - Explain why it can be dangerous to use the...Ch. 5.2 - The sales manager of a large company selected a...Ch. 5.2 - Explain why the slope b of the least-squares line...Ch. 5.2 - Prob. 34ECh. 5.3 - Does it pay to stay in school? The report Trends...Ch. 5.3 - The data in the accompanying table is from the...Ch. 5.3 - The paper referenced in the previous exercise also...Ch. 5.3 - Consider the residual plot from the previous...Ch. 5.3 - The report Airline Quality Rating 2016...Ch. 5.3 - Acrylamide is a chemical that is sometimes found...Ch. 5.3 - Consider the scatterplot of acrylamide...Ch. 5.3 - Some types of algae have the potential to cause...Ch. 5.3 - The relationship between x = Total number of...Ch. 5.3 - The residuals from the least-squares line for the...Ch. 5.3 - The first Batman movie was made over 50 years ago...Ch. 5.3 - The article 115K! The 13 Best Paying U.S....Ch. 5.3 - The article Examined Life: What Stanley H. Kaplan...Ch. 5.3 - The accompanying data are a subset of data from...Ch. 5.3 - The article California State Parks Closure List...Ch. 5.3 - The article referenced in the previous exercise...Ch. 5.3 - A study was carried out to investigate the...Ch. 5.3 - Both r2 and se are used to assess the fit of a...Ch. 5.3 - Prob. 53ECh. 5.4 - The following data on x = Frying time (in seconds)...Ch. 5.4 - Use the information provided in the previous...Ch. 5.4 - The paper Aspects of Food Finding by Wintering...Ch. 5.4 - Food intake of grazing animals is limited by the...Ch. 5.4 - A study, described in the paper Prediction of...Ch. 5.4 - Prob. 59ECh. 5.4 - The following table gives the number of heart...Ch. 5.4 - Refer to the heart transplant data given in the...Ch. 5.4 - The paper Population Pressure and Agricultural...Ch. 5.4 - Determining the age of an animal can sometimes be...Ch. 5.5 - The paper How Lead Exposure Relates to Temporal...Ch. 5.5 - The following quote is from the paper Evaluation...Ch. 5 - The accompanying data represent x = Amount of...Ch. 5 - The paper A Cross-National Relationship Between...Ch. 5 - The following data on x = Score on a measure of...Ch. 5 - The paper Effects of Canine Parvovirus (CPV) on...Ch. 5 - The paper Depression, Body Mass Index, and Chronic...Ch. 5 - The paper Aspects of Food Finding by Wintering...Ch. 5 - Data on salmon availability (x) and the percentage...Ch. 5 - No tortilla chip lover likes soggy chips, so it is...Ch. 5 - The article Reduction is Soluble Protein and...Ch. 5 - The following quote is from the paper The Weight...Ch. 5 - An accurate assessment of oxygen consumption...Ch. 5 - Consider the four (x, y) pairs (0, 0), (1, 1), 1,...Ch. 5 - Prob. 1CRECh. 5 - Data from a survey of 1046 adults age 50 and older...Ch. 5 - Prob. 3CRECh. 5 - Prob. 4CRECh. 5 - Prob. 5CRECh. 5 - The amount of money spent each year on science,...Ch. 5 - Below are the data used to construct the time...Ch. 5 - In August 2009, Harris Interactive released the...Ch. 5 - Prob. 9CRECh. 5 - Prob. 10CRECh. 5 - Prob. 11CRECh. 5 - Prob. 12CRECh. 5 - Cost-to-charge ratios (the percentage of the...Ch. 5 - In the article Reproductive Biology of the Aquatic...Ch. 5 - Prob. 15CRECh. 5 - Anabolic steroid abuse has been increasing despite...Ch. 5 - Prob. 81ECh. 5 - Prob. 82ECh. 5 - Prob. 83ECh. 5 - Prob. 84ECh. 5 - Suppose the hypothetical data below are from a...Ch. 5 - Prob. 86E
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