Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 13.2, Problem 20E
The paper “The Effects of Split Keyboard Geometry un Upper Body Postures” (Ergonomics [2009]: 104–111) describes a study to determine the effects of several keyboard characteristics on typing speed. One of the variables considered was the front-to-back surface angle of the keyboard. Minitab output resulting from fitting the simple linear regression model with x = Surface angle (degrees) and y = Typing speed (words per minute) is given below.
![Chapter 13.2, Problem 20E, The paper The Effects of Split Keyboard Geometry un Upper Body Postures (Ergonomics [2009]: 104111)](https://content.bartleby.com/tbms-images/9781337793612/Chapter-13/images/93612-13.2-20e-question-digital_image_001.png)
- a. Assuming that the basic assumptions of the simple linear regression model are reasonably met, carry out a hypothesis test to decide if there is a useful linear relationship between x and y. (Hint: See Example 13.5.)
- b. Are the values of se and r2 consistent with the conclusion from Part (a)? Explain.
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The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) through (c) below.
Click the icon to view the data table.
... .
(a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females.
Find the least-squares regression line for males.
y=x+O
Data for licensed drivers by age and gender.
%3D
(Round the x coefficient to three decimal places as needed. Round the constant to the nearest integer as needed.)
Find the least-squares regression line for females.
y =
Number of
Number o
X+
Number of Male Fatal
Number of Female Fatal
(Round the x coefficient to three decimal places as needed. Round the constant to the nearest integer as needed.)
Licensed Drivers Crashes
Licensed Drivers
Crashes
(b) Interpret the slope of the…
The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below.
Click the icon to view the data table.
C...
(a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for female
Find the least-squares regression line for males.
ŷ=0x+0
(Round the slope to three decimal places and round the constant to the nearest integer as needed.)
Data for licensed drivers by age and gender.
21-24
25-34
35-44
45-54
55-64
65-74
> 74
Number of Male Fatal
Licensed
Age Drivers (000s)
< 16
12
16-20
6,424
6,914
18,068
20,406
Number of
Number of Female Fatal
Crashes Licensed
(Males) Drivers (000s)
227
12
6,139
Crashes
(Females)
77
2,113
1,534
5,180
5,016
6,816
8,567
17,664
2,780
7,990
20,047
2,742
19,984
14,441
8,386
5,375
19,898
14,328
8,194…
Question 3. a) A Biologist is comparing intervals (m
seconds) between the matting calls of a certain species of
tree frog and the surrounding temperature (t degree
Celsius). The following results were obtained:
t 8 13 14 15
15
20
25
30
6.5
4.5
4
3
2
1
1. Fit the regression line in the form m = a + bt.
2. Interpret your estimates.
3. Use your regression line
interval between matting calls when the surrounding
temperature is 10 degrees. (6 marks)
estimate the time
Chapter 13 Solutions
Introduction To Statistics And Data Analysis
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- The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) through (c) below. Click the icon to view the data table. (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. (Round the x coefficient to three decimal places as needed. Round the constant to the nearest integer as needed.)arrow_forwardThe data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below. Click the icon to view the data table. (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. Data for licensed drivers by age and gender. y = x+ (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Find the least-squares regression line for females. y =x+ Number of Number of (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Number of Male Fatal Number of Female Fatal Licensed Drivers Crashes Licensed Drivers Crashes (b) Interpret the slope of the least-squares regression line for each gender, if…arrow_forwardIn a study of housing demand, the county assessor is interested in developing a regression model to estimate the market value (i.e., selling price) of residential property within his jurisdiction. The assessor feels that the most important variable affecting selling price (measured in thousands of dollars) is the size of house (measured in hundreds of square feet). He randomly selected 15 houses and measured both the selling price and size, as shown in the following table. OBSERVATIONi SELLING PRICE (× $1,000)Y SIZE (× 100 ft2 )X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 265.2 279.6 311.2 328.0 352.0 281.2 288.4 292.8 356.0 263.2 272.4 291.2 299.6 307.6 320.4 12.0 20.2 27.0 30.0 30.0 21.4 21.6 25.2 37.2 14.4 15.0 22.4 23.9 26.6 30.7 a. Plot the data.b. Determine the estimated regression line. Give an economic interpretation of the estimated slope (b) coefficient.c. Determine if size is a statistically significant variable in estimating selling price.d. Calculate the coefficient…arrow_forward
- Bill wants to explore factors affecting work stress. He would like to examine the relationship between age, number of years at the workplace, perceived social support, and work stress. He collects data on the variables from 100 employees (males and females) working in banks. The research question is How accurately can work stress be predicted from linear combination of the predictors (age, social support, number of years at the workplace)? Conduct a multiple regression analysis to answer the following questions: What is the relationship of age, number of years, and social support with work stress? Is the regression significant? If yes, what does it indicate?arrow_forwardBill wants to explore factors affecting work stress. He would like to examine the relationship between age, number of years at the workplace, perceived social support, and work stress. He collects data on the variables from 100 employees (males and females) working in banks. The research question is How accurately can work stress be predicted from linear combination of the predictors (age, social support, number of years at the workplace)? Conduct a multiple regression analysis to answer the following questions: What is the regression equation for all the predictors? Write a results section based on your analysis that answers the research question.arrow_forwardThe data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) through (c) below. Click the icon to view the data table. ..... (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. y =x+O %D/ (Round the x coefficient to three decimal places as needed. Round the constant to the nearest integer as needed.) Find the least-squares regression line for females. y = ý =x+O %3D (Round the x coefficient to three decimal places as needed. Round the constant to the nearest integer as needed.) (b) Interpret the slope of the least-squares regression line for each gender, if appropriate. How might an insurance company use this information? What is the correct interpretation of the…arrow_forward
- The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below. E Click the icon to view the data table. ked Бcor (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. Data for licensed drivers by age and gender. (Round the slope to three decimal places and round the constan ion estion 4 Number of Number of tion Number of Male Fatal Licensed Drivers Crashes Number of Female Fatal Licensed Drivers (000s) Crashes Age (000s) (Males) (Females) 74 4,803 2,022 5,375 973 Enter your answer in the edit fields and then click Check Ans Print Done parts remainingarrow_forwardSuppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept)HeightCabinets Estimate-57.98771.2760.3393 Std. Error8.63820.26430.1302 t value -6.7134.8282.607 Pr(>|t|)2.75e-074.44e-050.0145 10 Question 10 This is not a form; we suggest that you use the browse mode and read all parts of the question carefully. Which of the following is the correct interpretation of the coefficient for Cabinets? For a kitchen with a given ceiling height, the average number of cabinets…arrow_forwardSuppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept)HeightCabinets Estimate-57.98771.2760.3393 Std. Error8.63820.26430.1302 t value -6.7134.8282.607 Pr(>|t|)2.75e-074.44e-050.0145 Why is the interpretation of the constant term (i.e. "intercept") not meaningful for this example? The predicted area will be negative when the number of cabinets is zero and the height of the kitchen is also zero. But we cannot have a negative area, nor a kitchen ceiling height of 0 inches.…arrow_forward
- 13) Use computer software to find the multiple regression equation. Can the equation be used for prediction? An anti-smoking group used data in the table to relate the carbon monoxide( CO) of various brands of cigarettes to their tar and nicotine (NIC) content. 13). CO TAR NIC 15 1.2 16 15 1.2 16 17 1.0 16 6. 0.8 1 0.1 1 8. 0.8 8. 10 0.8 10 17 1.0 16 15 1.2 15 11 0.7 9. 18 1.4 18 16 1.0 15 10 0.8 9. 0.5 18 1.1 16 A) CO = 1.37 + 5.50TAR – 1.38NIC; Yes, because the P-value is high. B) CÓ = 1.37 - 5.53TAR + 1.33NIC; Yes, because the R2 is high. C) CO = 1.25 + 1.55TAR – 5.79NIC; Yes, because the P-value is too low. D) CO = 1.3 + 5.5TAR - 1.3NIC; Yes, because the adjusted R2 is high. %3Darrow_forwardSuppose researchers are interested in exploring the factors which affect depression for Australian adults. The researchers recruited a sample of 99 Australian adults and collected data on several variables which may influence depression. Note that here depression is represented by a score, with higher values representing higher levels of depression. The variables for this study are listed below: Age Gender (0 = female, 1 = male) Stress level Anxiety level Depression Why would conducting a multiple linear regression analysis be appropriate here? Group of answer choices A) Multiple linear regression can be appropriate here because we have one metric dependent variable and several metric or dichotomous independent variables B) Multiple linear regression can be appropriate here because we have one metric dependent variable and several categorical independent variables C) Multiple linear regression can be appropriate here because we have one categorical dependent variable and…arrow_forwardWe have data on Lung Capacity of persons and we wish to build a multiple linear regression model that predicts Lung Capacity based on the predictors Age and Smoking Status. Age is a numeric variable whereas Smoke is a categorical variable (0 if non-smoker, 1 if smoker). Here is the partial result from STATISTICA. b* Std.Err. of b* Std.Err. N=725 of b Intercept Age Smoke 0.835543 -0.075120 1.085725 0.555396 0.182989 0.014378 0.021631 0.021631 -0.648588 0.186761 Which of the following statements is absolutely false? A. The expected lung capacity of a smoker is expected to be 0.648588 lower than that of a non-smoker. B. The predictor variables Age and Smoker both contribute significantly to the model. C. For every one year that a person gets older, the lung capacity is expected to increase by 0.555396 units, holding smoker status constant. D. For every one unit increase in smoker status, lung capacity is expected to decrease by 0.648588 units, holding age constant.arrow_forward
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