Question 4 When Y is regressed on X, B, > 0, sx+ 0, sy # 0, and the fraction of the variation in Y explainedby the least-squares regression of Y on X does not equal 1. In this example, the sum of thesquares of the deviations of the actual Y-values from their mean would definitely be greater thanthe sum of the squares of the deviations of the predicted Y-values from their mean.1A)B)truefalse4.When Y is regressed on X, the sample slope is negative, sx + 0, sy + 0, and Y; = Y; for everyobservation. In this example, the sum of the squares of the deviations of the predicted Y-valuesfrom their mean would definitely be less than the sum of the squares of the deviations of theactual Y-values from their mean.A)В)truefalse3.

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When Y is regressed on X, B, >0, Sx# 0, sy± 0, and the fraction of the variation in Y explained by the least-squares regression of Y on X does not equal 1. In this example, the sum of the squares of the deviations of the actual Y-values from their mean would definitely be greater than the sum of the squares of the deviations of the predicted Y-values from their mean. true false When Y is regressed on X, the sample slope is negative, Sx#0, sy± 0, and Y; = Ý; for every observation. In this example, the sum of the squares of the deviations of the predicted Y-values from their mean would definitely be less than the sum of the squares of the deviations of the actual Y-values from their mean. true false

When Y is regressed on X, B, >0, Sx# 0, sy± 0, and the fraction of the variation in Y explained by the least-squares regression of Y on X does not equal 1. In this example, the sum of the squares of the deviations of the actual Y-values from their mean would definitely be greater than the sum of the squares of the deviations of the predicted Y-values from their mean. true false When Y is regressed on X, the sample slope is negative, Sx#0, sy± 0, and Y; = Ý; for every observation. In this example, the sum of the squares of the deviations of the predicted Y-values from their mean would definitely be less than the sum of the squares of the deviations of the actual Y-values from their mean. true false

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy

Problem 1EA

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If 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?
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?
Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
The weight (in pounds) and height (in inches) for a child were measured every few months over a two- The equation ý = 17.4 + 0.5x is called the least- squares regression line because it year period. The results are displayed in the scatterplot. O is least able to make accurate predictions for the data. O makes the strongest association between weight and height. A Child's Weight and Height 40 O minimizes the sum of the squared distances from the actual y-value to the predicted y-value. 36 O maximizes the sum of the squared distances from the actual y-value to the predicted y-value. 32 28 24 20 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 4042 Weight (Pounds) Height (Inches)
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=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…
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= 82.15 – 0.47x. 00 Birthrate, x Female life expectancy, y (in years) (number of births per 1000 people) 40.4 65.2 85- 50.4 59.0 80+ 18.4 71.6 75- 26.5 69.9 70 32.0 64.5 65- 51.7 52.9 60- 34.4 67.2 14.6 75.9 50.1 45.8 59.2 49.9 62.1 Birthrate 73.7 26.2 (number of births per 1000 people) 73.7 14.4 Save For Later Submit Assignment Check 2 Accessibility O 2022 McGraw Hill LLC AN Rights Reserved. Terms of Use / Privacy Center DO 80 DIl 110 17 Da SO FA F4 esc F2 & delete %24 % 8 %23 6 7 3 4 7. U T K LA G S D Female life expectancy (in years)
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 = 82.76 -0.50x. Birthrate, x (number of births per 1000 people) 20.5 39.4 46.5 52.8 26.5 35.2 47.1 49.1 23.6 31.9 15.6 13.9 Send data to calculator V Female life expectancy, y (in years) 72.7 65.1 58.1 57.9 72.2 67.5 60.8 53.3 73.3 64.0 72.1 75.0 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 xx 10 15 20 25 30 x than (b) According to the regression equation, for an increase of one (birth per 1000 people) in birthrate, there is a corresponding decrease of how many…
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 = 82.60-0.48x. Birthrate, x (number of births per 1000 people) 31.7 14.3 49.4 23.2 27.7 19.3 40.0 49.1 46.0 52.5 14.1 35.5 Send data to calculator V Female life expectancy, y (in years) 61.8 75.5 54.8 73.7 72.9 73.2 65.9 62.1 58.1 58.5 73.9 68.6 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 xx 15 20 25 X (b) According to the regression equation, for an increase of one (birth per 1000 people) in birthrate, there is a corresponding decrease of how many years in female…
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 = 82.17 -0.47x. Birthrate, x (number of births per 1000 people) 14.3 27.4 51.1 46.8 24.9 29.9 18.2 41.6 49.4 14.1 33.9 49.3 Send data to calculator Female life expectancy, y (in years) 75.6 70.5 58.2 59.0 73.3 62.7 73.6 65.2 62.4 74.3 67.0 53.9 Send data to Excel Female life expectancy (In years) Based on the sample data and the regression line, answer the following. 85+ 80+ 75+ 70+ 65 60 55+ 50 (a) From the regression equation, what is the predicted female life expectancy (in years) when the birthrate is 29.9 births per 1000 people? Round your answer to…
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 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.) .
The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are displayed in the scatterplot. The equation ŷ = 17.4 + 0.5x is called the least-squares regression line because it is least able to make accurate predictions for the data. A Child's Weight and Height makes the strongest association between weight and 40 height. 36 minimizes the sum of the squared distances from the actual y-value to the predicted y-value. 32 maximizes the sum of the squared distances from the actual y-value to the predicted y-value. 20 24 20 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 Weight (Pounds) Height (Inches)
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…