Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year old baby and the weight y of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females. x (lb) 22 26 21 23 20 15 25 21 17 24 26 22 18 19 y (lb) 130 124 115 130 130 120 145 130 130 130 130 140 110 115 In this setting we have Σx = 299, Σy = 1779, Σx2 = 6531, Σy2 = 227,251, and Σxy = 38,199. (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your answers for least-squares estimates to four decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y). (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) %(d) Test the claim that the population correlation coefficient ρ is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. P-value > 0.2500.125 < P-value < 0.250 0.100 < P-value < 0.1250.075 < P-value < 0.1000.050 < P-value < 0.0750.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.0100.0005 < P-value < 0.005P-value < 0.0005 Conclusion Reject the null hypothesis. There is sufficient evidence that ρ > 0.Reject the null hypothesis. There is insufficient evidence that ρ > 0. Fail to reject the null hypothesis. There is sufficient evidence that ρ > 0.Fail to reject the null hypothesis. There is insufficient evidence that ρ > 0. (e) If a female baby weighs 15 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) lb(f) Find Se. (Round your answer to two decimal places.)Se = (g) Find a 95% confidence interval for weight at age 30 of a female who weighed 15 pounds at 1 year of age. (Round your answers to two decimal places.) lower limit lb upper limit lb (h) Test the claim that the slope β of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. P-value > 0.2500.125 < P-value < 0.250 0.100 < P-value < 0.1250.075 < P-value < 0.1000.050 < P-value < 0.0750.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.0100.0005 < P-value < 0.005P-value < 0.0005 Conclusion Reject the null hypothesis. There is sufficient evidence that β > 0.Reject the null hypothesis. There is insufficient evidence that β > 0. Fail to reject the null hypothesis. There is sufficient evidence that β > 0.Fail to reject the null hypothesis. There is insufficient evidence that β > 0. (i) Find an 80% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.) lower limit upper limit Interpretation For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval.For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval. For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval.For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval.
Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year old baby and the weight y of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females. x (lb) 22 26 21 23 20 15 25 21 17 24 26 22 18 19 y (lb) 130 124 115 130 130 120 145 130 130 130 130 140 110 115 In this setting we have Σx = 299, Σy = 1779, Σx2 = 6531, Σy2 = 227,251, and Σxy = 38,199. (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your answers for least-squares estimates to four decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y). (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) %(d) Test the claim that the population correlation coefficient ρ is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. P-value > 0.2500.125 < P-value < 0.250 0.100 < P-value < 0.1250.075 < P-value < 0.1000.050 < P-value < 0.0750.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.0100.0005 < P-value < 0.005P-value < 0.0005 Conclusion Reject the null hypothesis. There is sufficient evidence that ρ > 0.Reject the null hypothesis. There is insufficient evidence that ρ > 0. Fail to reject the null hypothesis. There is sufficient evidence that ρ > 0.Fail to reject the null hypothesis. There is insufficient evidence that ρ > 0. (e) If a female baby weighs 15 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) lb(f) Find Se. (Round your answer to two decimal places.)Se = (g) Find a 95% confidence interval for weight at age 30 of a female who weighed 15 pounds at 1 year of age. (Round your answers to two decimal places.) lower limit lb upper limit lb (h) Test the claim that the slope β of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. P-value > 0.2500.125 < P-value < 0.250 0.100 < P-value < 0.1250.075 < P-value < 0.1000.050 < P-value < 0.0750.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.0100.0005 < P-value < 0.005P-value < 0.0005 Conclusion Reject the null hypothesis. There is sufficient evidence that β > 0.Reject the null hypothesis. There is insufficient evidence that β > 0. Fail to reject the null hypothesis. There is sufficient evidence that β > 0.Fail to reject the null hypothesis. There is insufficient evidence that β > 0. (i) Find an 80% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.) lower limit upper limit Interpretation For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval.For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval. For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval.For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Concept explainers
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Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
Modern medical practice tells us not to encourage babies to become too fat. Is there a
| x (lb) | 22 | 26 | 21 | 23 | 20 | 15 | 25 | 21 | 17 | 24 | 26 | 22 | 18 | 19 |
| y (lb) | 130 | 124 | 115 | 130 | 130 | 120 | 145 | 130 | 130 | 130 | 130 | 140 | 110 | 115 |
In this setting we have Σx = 299, Σy = 1779, Σx2 = 6531, Σy2 = 227,251, and Σxy = 38,199.
(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your answers for least-squares estimates to four decimal places.)
(b) Draw ascatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y).
(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)
What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
%
(d) Test the claim that the population correlation coefficient ρ is positive at the 1% level of significance. (Round your test statistic to three decimal places.)
Find or estimate the P-value of the test statistic.
Conclusion
(e) If a female baby weighs 15 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.)
lb
(f) Find Se. (Round your answer to two decimal places.)
Se =
(g) Find a 95% confidence interval for weight at age 30 of a female who weighed 15 pounds at 1 year of age. (Round your answers to two decimal places.)
(h) Test the claim that the slope β of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.)
Find or estimate the P-value of the test statistic.
Conclusion
(i) Find an 80% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.)
Interpretation
| x | = | |
| y | = | |
| b | = | |
| ŷ | = | + x |
(b) Draw a
(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)
| r = | |
| r2 = |
What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
%
(d) Test the claim that the population correlation coefficient ρ is positive at the 1% level of significance. (Round your test statistic to three decimal places.)
t =
Find or estimate the P-value of the test statistic.
P-value > 0.2500.125 < P-value < 0.250 0.100 < P-value < 0.1250.075 < P-value < 0.1000.050 < P-value < 0.0750.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.0100.0005 < P-value < 0.005P-value < 0.0005
Conclusion
Reject the null hypothesis. There is sufficient evidence that ρ > 0.Reject the null hypothesis. There is insufficient evidence that ρ > 0. Fail to reject the null hypothesis. There is sufficient evidence that ρ > 0.Fail to reject the null hypothesis. There is insufficient evidence that ρ > 0.
(e) If a female baby weighs 15 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.)
lb
(f) Find Se. (Round your answer to two decimal places.)
Se =
(g) Find a 95% confidence interval for weight at age 30 of a female who weighed 15 pounds at 1 year of age. (Round your answers to two decimal places.)
| lower limit | lb |
| upper limit | lb |
(h) Test the claim that the slope β of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.)
t =
Find or estimate the P-value of the test statistic.
P-value > 0.2500.125 < P-value < 0.250 0.100 < P-value < 0.1250.075 < P-value < 0.1000.050 < P-value < 0.0750.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.0100.0005 < P-value < 0.005P-value < 0.0005
Conclusion
Reject the null hypothesis. There is sufficient evidence that β > 0.Reject the null hypothesis. There is insufficient evidence that β > 0. Fail to reject the null hypothesis. There is sufficient evidence that β > 0.Fail to reject the null hypothesis. There is insufficient evidence that β > 0.
(i) Find an 80% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.)
| lower limit | |
| upper limit |
Interpretation
For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval.For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval. For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval.For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval.
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