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What percentage of the variation in  can be explained by the corresponding variations in  and  taken together

What percentage of the variation in  can be explained by the corresponding variations in  and  taken together

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
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What percentage of the variation in  can be explained by the corresponding variations in  and  taken together?

The systolic blood pressure of individuals is thought to be related to both age and weight. Let the systolic blood pressure, age, and weight be represented by the variables x1, x2, and x3, respectively. Suppose that Minitab was used to generate the following descriptive statistics, correlations, and regression analysis for a random sample of 15 individuals. Descriptive Statistics Variable Mean Median TrMean StDev SE Mean 0.997939 0.400725 15 157.77 158.27 157.77 .865 15 55.94 56.34 55.94 1.552 X3 15 177.11 176.41 177.11 4.125 1.065070 Variable Minimum Маximum Q1 Q3 128 171 140.378 167.716 Ix 83 44 47.594 77.730 223.140 123 236 143.057 Correlations (Pearson) Ix 0.855 0.885 0.681 Ex Regression Analysis The regression equation is x1 = 0.557 + 1.117x2 + 0.808x3 Coef Predictor Constant StDev IT P 0.557 0.383 1.45 0.086 x2 1.117 0.753 1.48 0.082 0.808 0.018 2.36 R-sq(adj) = 93.8 % 0.343 S = 0.142 R-sq = 96.6 % What percentage of the variation in xị can be explained by the corresponding variations in x2 and x3 taken together? O 88.5 % O 68.1 % O 93.8 % O 96.6% O 85.5%
Transcribed Image Text:The systolic blood pressure of individuals is thought to be related to both age and weight. Let the systolic blood pressure, age, and weight be represented by the variables x1, x2, and x3, respectively. Suppose that Minitab was used to generate the following descriptive statistics, correlations, and regression analysis for a random sample of 15 individuals. Descriptive Statistics Variable Mean Median TrMean StDev SE Mean 0.997939 0.400725 15 157.77 158.27 157.77 .865 15 55.94 56.34 55.94 1.552 X3 15 177.11 176.41 177.11 4.125 1.065070 Variable Minimum Маximum Q1 Q3 128 171 140.378 167.716 Ix 83 44 47.594 77.730 223.140 123 236 143.057 Correlations (Pearson) Ix 0.855 0.885 0.681 Ex Regression Analysis The regression equation is x1 = 0.557 + 1.117x2 + 0.808x3 Coef Predictor Constant StDev IT P 0.557 0.383 1.45 0.086 x2 1.117 0.753 1.48 0.082 0.808 0.018 2.36 R-sq(adj) = 93.8 % 0.343 S = 0.142 R-sq = 96.6 % What percentage of the variation in xị can be explained by the corresponding variations in x2 and x3 taken together? O 88.5 % O 68.1 % O 93.8 % O 96.6% O 85.5%
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