Student's Solution and Survival Manual for Calculus
7th Edition
ISBN: 9781524934040
Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J
Publisher: Kendall Hunt Publishing
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Concept explainers
Question
Chapter 11.7, Problem 31PS
To determine
The least square regression line.
Expert Solution & Answer
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Check out a sample textbook solutionStudents have asked these similar questions
The equation Y= α+ βx+ε describes a population regression line. Which of the statements regarding this equation is true.
A. ε is the coefficient of standard deviation
B. α,β are sample statistics that can be calculated by the ordinary least squares method
C. α,β are usually unknown since they are population quantities
D. None of the statements above are true
John’s parents recorded his height at various ages up to 66 months. Below is a record of the results.
Age (months)
36
48
54
60
66
Height (inches)
35
38
41
43
45
John’s parents decide to use the least-squares regression line of John’s height on age based on the data in the previous problem to predict his height at age 21 years (252 months). We conclude
#3. What is the least squares regression line for the following set of data?
y-hat = 2.18x + 27.74
y-hat = 2.14x + 27.44
y-hat = 1.94x + 26.24
y-hat =1.86x + 26.28
Chapter 11 Solutions
Student's Solution and Survival Manual for Calculus
Ch. 11.1 - Prob. 1PSCh. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Prob. 7PSCh. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Prob. 10PS
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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_forwardIf 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_forward
- Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y = 81.87– 0.46x. Birthrate, x (number of births per 1000 рop.) Female life expectancy, y (in years) 85- 35.7 67.7 80 41.5 63.9 31.9 63.3 75+ メメ 19.9 73.0 70- 50.5 60.4 65- 24.4 72.7 60- 50.1 63.2 55 13.8 72.5 50 50.3 54.6 45.6 57.9 15.9 76.2 Figure 1 26.6 71.9arrow_forwardBelow are bivariate data O each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is ing birthrate and life expectancy information for y = 81.87 – 0.46x. Birthrate, x (number of births per 1000 pop.) Female life expectancy, y (in years) 85- 35.7 67.7 80- 41.5 63.9 75 31.9 63.3 19.9 73.0 70 50.5 60.4 65. 24.4 72.7 60- 50.1 63.2 55 13.8 72.5 50 50.3 54.6 45.6 57.9 15.9 76.2 Figure 1 26.6 71.9 Send data to Excelarrow_forwardIf the point representing 64 wins and attendance of 40,786, people per game is removed from the set of data and a new regression analysis is conducted, how would the following be mpacted?arrow_forward
- Might we be able to predict life expectancies from birthrates? Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y=83.86-0.52x. Birthrate, x Female life expectancy, y (in years) (number of births per 1000 people) 34.4 67.3 19.6 72.9 49.2 58.8 XX 39.4 63.8 28.0 73.3 50.3 53.9 14.1 77.3 15.5 73.3 45.0 57.8 30.8 63.2 50.6 61.8 26.0 73.3 Send data to calculator V Based on the sample data and the regression line, answer the following. (a) From the regression equation, what is the predicted female life expectancy (in years) when the birthrate is 30.8 births per 1000 people? Round your answer to one or more decimal places. (b) From the regression equation, what is the…arrow_forwardMight we be able to predict life expectancies from birthrates? Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y = 81.92-0.47x. Birthrate, x Female life expectancy, y (in years) (number of births per 1000 people) 34.3 65.7 42.5 64.5 13.3 71.3 xx 19.1 72.3 45.0 60.0 32.9 62.5 14.7 75.9 50.4 58.4 49.7 53.3 24.2 74.3 49.7 61.3 27.8 73.5 Send data to calculator V Send data to Excel Based on the sample data and the regression line, answer the following. (a) From the regression equation, what is the predicted female life expectancy (in years) when the birthrate is 45.0 births per 1000 people? Round your answer to one or more decimal places. 0 (b) What was the observed…arrow_forwardMight we be able to predict life expectancies from birthrates? Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y =81.68 –0.47x. Birthrate, x Female life expectancy, y (in years) (number of births per 1000 people) 85 50.7 54.3 80 + 46.1 56.5 18.3 72.7 75 + 26.1 73.3 70. 13.8 72.4 65 + 27.5 71.9 60 - 49.8 60.0 55 - 15.2 75.0 50 32.0 62.3 20 30 35 40 45 34.6 65.8 49.7 61.5 Birthrate (number of births per 1000 people) 40.4 65.4 Send data to calculator Based on the sample data and the regression line, complete the following. (a) For these data, birthrates that are greater than the mean of the birthrates tend to be paired with female life ? expectancies that are (Choose…arrow_forward
- Might we be able to predict life expectancies from birthrates? Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y=81.85-0.46x. Birthrate, x Female life expectancy, y (in years) (number of births per 1000 people) 15.2 71.5 50.8 61.6 31.3 63.9 26.1 73.8 x 46.1 57.8 33.4 66.4 18.7 71.7 27.1 71.0 51.3 53.7 51.7 59.6 40.8 65.6 15.5 77.0 Send data to calculator Send data to Excel Based on the sample data and the regression line, answer the following. (a) From the regression equation, what is the predicted female life expectancy (in years) when the birthrate is 15.2 births per 1000 people? Round your answer to one or more decimal places. 0 (b) What was the observed female…arrow_forwardMight we be able to predict life expectancies from birthrates? Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y=82.25 -0.48x. ^ Birthrate, x (number of births per 1000 people) 35.5 44.9 29.7 19.9 13.7 27.0 51.9 15.0 50.9 49.7 39.6 24.4 Send data to calculator Send data to Excel Female life expectancy, y (in years) 67.9 57.9 61.7 71.4 72.5 73.5 55.4 76.5 58.2 60.6 64.4 74.4 Based on the sample data and the regression line, complete the following. Female life expectancy (in years) 85 80+ 75+ 70- 65+ 60- 55+ 50 x X x ++ 10 15 20 25 (b) According to the regression equation, for an increase of one (birth per 1000 people) in birthrate, there is a corresponding decrease…arrow_forwardMight we be able to predict life expectancies from birthrates?Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is Ŷ=82.24-0.48x (The 2nd picture contains the rest of the data as it would not fit in the first pic and it includes the question as well.) .arrow_forward
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