Pearson eText Business Statistics: First Course -- Instant Access (Pearson+)
8th Edition
ISBN: 9780136880974
Author: David Levine, David Stephan
Publisher: PEARSON+
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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) to (c) below.
.....
(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.
(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.
x +
Number of
Number of
Number of Male Fatal
Number of Female Fatal
(Round the slope to three decimal places and round the constant to the nearest integer as needed.)
Licensed Drivers Crashes
Licensed Drivers
Crashes
(b) Interpret the slope of the least-squares regression line for each gender, if appropriate. How might an insurance…
An article on the cost of housing in California† included the following statement: "In Northern California, people from the San Francisco Bay area pushed into the Central Valley, benefiting from home prices that dropped on average $4,000 for every mile traveled east of the Bay." If this statement is correct, what is the slope of the least-squares regression line,
ŷ = a + bx,
where
y = house
price (in dollars) and
x = distance
east of the Bay (in miles)?
Explain.
This value is the change in the distance east of the bay, in miles, for each increase of $1 in average home price.This value is the change in the distance east of the bay, in miles, for each decrease of $1 in average home price. This value is the change in the average home price, in dollars, for each increase of 1 mile in the distance east of the bay.This value is the change in the average home price, in dollars, for each decrease of 1 mile in the distance east of the bay.
The relationship between total cholesterol (milligrams per deciliter) and BMI (Ratio of weight in kilograms to height in metres squared) of 20 participants
is shown in the scatterplot below along with the least squares regression line.
Which of the following statements is correct?
a) The relationship between total cholesterol and BMI is linear as can be seen by the random scatter of the data above and below the least squares regression line.
Both variables are metric and therefore it is appropriate to use Pearson's correlation to measure the linear association between the two variables.
b) The relationship between total cholesterol and BMI is non-linear and since both variables are metric it is appropriate to use Pearson's correlation to measure the linear association between the two variables.
c) The relationship between total cholesterol and BMI is non-linear as can be seen by the patterning of points around the least squares regression line and therefore it is not…
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardOlympic 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_forwardA pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the accompanying data. Complete parts (a) through (g) below. Click the icon to view the children's data. (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. y=x+ (Round the slope to three decimal places and round the constant to one decimal place as needed.) (b) Interpret the slope and y-intercept, if appropriate. First interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. For every inch increase in head circumference, the height increases by in., on average. (Round to three decimal places as needed.) OB. For a height of 0 inches, the head circumference is predicted to be in. (Round to three decimal places as…arrow_forward
- 4. We would like to determine how a man's weight can be used to predict his systolic blood pressure. We measure the weights (in pounds) and the systolic blood pressures of a sample of 17 men. The data are plotted on a scatterplot and it can be seen that a linear relationship is a reasonable assumption. The least squares regression line is calculated to be ŷ = 125.561 + 0.145x. The ANOVA table (with some values missing) is shown below: |Source of Variation | df | Sum of Squares Mean Square F Regression Error Total 26.46 617.82 (a) We would like to test whether a linear relationship exists between a man's weight and his systolic blood pressure. We will conduct an analysis of variance to test Ho: B1 = 0 vs. Ha: B1 + 0 at the 5% level of significance. Enter all missing values in the ANOVA table. Calculate the value of the test statistic, find the P-value of the test and provide a properly worded conclusion. (b) What is the value of the correlation between weight and systolic blood pressure…arrow_forward4. A simple linear regression is fit to a dataset. Unfortunately, the corresponding ANOVA table is not complete because some quantities in the table are missing due to unknown digital errors. Calculate the missing values, denoted by "?", in the ANOVA table based on the other available values. Is this regression model significant (α = 0.05)? Source Regression Residual Total df ? ? 21 SS ? ? ? MS = SS/df ? 1.13 F-Ratio 430.65 p-value ?arrow_forwardIn comparing two multiple regression models, one with variables that are a subset of the other, bigger model’s variables, to infer which model is superior, I get confused in looking at R-squared, adjusted R-squared, and F-statistic values. What’s the difference among them and is one of these preferable to the others? Thanks.arrow_forward
- A drug company wants to test a new cancer drug to find out if it improves life expectancy. Patients were randomized to receive a placebo or the new cancer drug. What Is the most suitable statistical test for this research? a.Two-sample T-Test b. Paired T-Test c. ANOVA d.Linear Regressionarrow_forwardPolice sometimes use footprint evidence to estimate the height of a suspect. Data was collected from 36 randomly selected men in Nebraska in 2001. The regression model assumptions have been checked, and they are all satisfied. We want to test if there is a positive linear association between shoe print size and average height. The p-value of the appropriate test was found to be 0.0006. (a) Give your brief conclusion. Note that no significance level is provided. (b) Give your conclusion in the context of the problem. (This question will be marked manually by your instructor).arrow_forwardDo you think the regression in Table 5 suffers from omitted variable bias? If yes,which additional variables would you include to control for omitted variable bias?arrow_forward
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