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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 N Mean Median TrMean StDev SE Mean x1 15 158.78 159.68 158.78 3.459 0.893110 x2 15 56.85 57.85 56.85 1.445 0.373097 x3 15 176.84 176.04 176.84 4.018 1.037443 ​ Variable Minimum Maximum Q1 Q3 x1 126 170 136.347 167.113 x2 43 81 47.839 77.990 x3 120 234 141.672 224.477 ​ Correlations (Pearson)   x1 x2 x2 0.889   x3 0.850 0.639 Regression Analysis   The regression equation is   x1 = 0.808 + 1.262x2 + 0.815x3  ​ Predictor Coef StDev T P Constant 0.808 0.494 1.64 0.064 x2 1.262 0.617 2.05 0.032 x3 0.815 0.753 1.08 0.150 S = 0.470 R-sq = 91.1 % R-sq(adj) = 93.1 %     ​ What percentage of variation in x1 can be explained by the corresponding variation in x2?  Round your answer to the nearest tenth. answer choices: 91.1% 93.1% 8.9% 72.3% 79.0%

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 N Mean Median TrMean StDev SE Mean x1 15 158.78 159.68 158.78 3.459 0.893110 x2 15 56.85 57.85 56.85 1.445 0.373097 x3 15 176.84 176.04 176.84 4.018 1.037443 ​ Variable Minimum Maximum Q1 Q3 x1 126 170 136.347 167.113 x2 43 81 47.839 77.990 x3 120 234 141.672 224.477 ​ Correlations (Pearson)   x1 x2 x2 0.889   x3 0.850 0.639 Regression Analysis   The regression equation is   x1 = 0.808 + 1.262x2 + 0.815x3  ​ Predictor Coef StDev T P Constant 0.808 0.494 1.64 0.064 x2 1.262 0.617 2.05 0.032 x3 0.815 0.753 1.08 0.150 S = 0.470 R-sq = 91.1 % R-sq(adj) = 93.1 %     ​ What percentage of variation in x1 can be explained by the corresponding variation in x2?  Round your answer to the nearest tenth. answer choices: 91.1% 93.1% 8.9% 72.3% 79.0%

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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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 N Mean Median TrMean StDev SE Mean
x1 15 158.78 159.68 158.78 3.459 0.893110
x2 15 56.85 57.85 56.85 1.445 0.373097
x3 15 176.84 176.04 176.84 4.018 1.037443

​

Variable Minimum Maximum Q1 Q3
x1 126 170 136.347 167.113
x2 43 81 47.839 77.990
x3 120 234 141.672 224.477

​

Correlations (Pearson)
  x1 x2
x2 0.889  
x3 0.850 0.639

Regression Analysis
 

The regression equation is
 

x1 = 0.808 + 1.262x2 + 0.815x3 

​

Predictor Coef StDev T P
Constant 0.808 0.494 1.64 0.064
x2 1.262 0.617 2.05 0.032
x3 0.815 0.753 1.08 0.150
S = 0.470 R-sq = 91.1 % R-sq(adj) = 93.1 %    

​

What percentage of variation in x1 can be explained by the corresponding variation in x2?  Round your answer to the nearest tenth.

answer choices:

91.1%

93.1%

8.9%

72.3%

79.0%

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