Question

In: Statistics and Probability

The data show systolic and diastolic blood pressure of certain people. Find the regression​ equation, letting...

The data show systolic and diastolic blood pressure of certain people. Find the regression​ equation, letting the systolic reading be the independent​ (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 137. Is the predicted value close to 97.1​, which was the actual diastolic​ reading? Use a significance level of 0.05. Systolic 129 119 126 145 126 125 142 110 Diastolic 94 64 68 84 93 91 104 79

What is the regression​ equation?

Solutions

Expert Solution

Sum of X = 1022
Sum of Y = 677
Mean X = 127.75
Mean Y = 84.625
Sum of squares (SSX) = 907.5
Sum of products (SP) = 554.25

Regression Equation = ŷ = bX + a

b = SP/SSX = 554.25/907.5 = 0.6107

a = MY - bMX = 84.63 - (0.61*127.75) = 6.6025

ŷ = 0.6107X + 6.6025

X Values
∑ = 1022
Mean = 127.75
∑(X - Mx)2 = SSx = 907.5

Y Values
∑ = 677
Mean = 84.625
∑(Y - My)2 = SSy = 1307.875

X and Y Combined
N = 8
∑(X - Mx)(Y - My) = 554.25

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 554.25 / √((907.5)(1307.875)) = 0.5087

The sample size is n = 8n=8, so then the number of degrees of freedom is df=n−2=8−2=6

The corresponding critical correlation value rc​ for a significance level of α=0.05, for a two-tailed test is:

rc​=0.707

Observe that in this case, the null hypothesis is rejected if ∣r∣>rc​=0.707.

Here r>rc, so test is significant

For x=137,

ŷ = (0.6107*137) + 6.6025=90.2684

It is different from 91.7


Related Solutions

The data show systolic and diastolic blood pressure of certain people. Find the regression​ equation, letting...
The data show systolic and diastolic blood pressure of certain people. Find the regression​ equation, letting the systolic reading be the independent​ (x) variable. If one of these people has a systolic blood pressure of 113mm​ Hg, what is the best predicted diastolic blood​ pressure? systolic: 150 129 142 112 134 122 126 120 diastolic: 88 96 106 80 98 63 95 64 y = _ + _X
The data show systolic and diastolic blood pressure of certain people. Find the regression​ equation, letting...
The data show systolic and diastolic blood pressure of certain people. Find the regression​ equation, letting the systolic reading be the independent​ (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 127127. Is the predicted value close to 96.696.6​, which was the actual diastolic​ reading? Use a significance level of 0.05. Systolic 135135 125125 114114 143143 130130 135135 126126 117117 Diastolic 9898 6868 8282 102102 7070 101101 9494 5858 LOADING... Click the icon...
The data show systolic and diastolic blood pressure of certain people. Find the regression​ equation, letting...
The data show systolic and diastolic blood pressure of certain people. Find the regression​ equation, letting the systolic reading be the independent​ (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 150. Is the predicted value close to 66.2​, which was the actual diastolic​ reading? Use a significance level of 0.05. Systolic 139 118 145 133 141 138 139 136    Diastolic 101 61 82 74 104 79 74 74 LOADING... Click the...
The data show systolic and diastolic blood pressure of certain people. A) Find the regression​ equation,...
The data show systolic and diastolic blood pressure of certain people. A) Find the regression​ equation, letting the systolic reading be the independent​ (x) variable. B) Find the best predicted diastolic pressure for a person with a systolic reading of 148. C)Is the predicted value close to 64.1​, which was the actual diastolic​ reading? Use a significance level of 0.05. Systolic 139 112 113 150 129 112 128 139    Diastolic 102 83 57 87 72 80 67 74
The data show the systolic and diastolic blood pressure readings for 12 women.
The data show the systolic and diastolic blood pressure readings for 12 women.         X=Systolic      123      116      82        126      116      138      109      119      155      106      178      84       Y=Diastolic    66      71      62        84      70      91      67      66      80       70       89        72         a….What is the Y-INTERCEPT of the Least-Squares regression equation?       b…..Predict the diastolic reading for a woman whose systolic reading is 165.       c…..What percent of the variation in diastolic pressure is due to factors...
The data show the chest size and weight of several bears. Find the regression​ equation, letting...
The data show the chest size and weight of several bears. Find the regression​ equation, letting chest size be the independent​ (x) variable. Then find the best predicted weight of a bear with a chest size of 51 inches. Is the result close to the actual weight of 342 ​pounds? Use a significance level of 0.05. Chest size​ (inches) 45 50 43 43 52 52 Weight​ (pounds) 352 374 275 314 440 367 What is the regression equation? y=___+___x (round...
The data show the chest size and weight of several bears. Find the regression​ equation, letting...
The data show the chest size and weight of several bears. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Then find the best predicted weight of a bear with a chest size of 41 inches. Use a significance level of 0.05. Chest size (inches)   Weight (pounds) 40   227 53   360 38   153 43   206 44   234 58   414 What is the regression​ equation? What is the best predicted​ value?
The data show the chest size and weight of several bears. Find the regression​ equation, letting...
The data show the chest size and weight of several bears. Find the regression​ equation, letting chest size be the independent​ (x) variable. Then find the best predicted weight of a bear with a chest size of 50 inches. Is the result close to the actual weight of 427 pounds? Use a significance level of 0.05. Chest_size_(inches)   Weight_ (pounds) 49   368 51   382 53   420 61   481 57   457 45   287 What is the regression​ equation? What is the best...
The data show the chest size and weight of several bears. Find the regression​ equation, letting...
The data show the chest size and weight of several bears. Find the regression​ equation, letting chest size be the independent​ (x) variable. Then find the best predicted weight of a bear with a chest size of 51 inches. Is the result close to the actual weight of 585 ​pounds? Use a significance level of 0.05. Chest size​ (inches) 47 46 49 50 38 48 Weight​ (pounds) 487 496 546 518 397 510 a) what is the regression equation? b)...
The data show the chest size and weight of several bears. Find the regression​ equation, letting...
The data show the chest size and weight of several bears. Find the regression​ equation, letting chest size be the independent​ (x) variable. Then find the best predicted weight of a bear with a chest size of 3939 inches. Is the result close to the actual weight of 126126 ​pounds? Use a significance level of 0.05. Chest size​ (inches) 44 41 41 55 51 42 Weight​ (pounds) 213 206 176 309 300 178 n alphaαequals=0.05 alphaαequals=0.01 ​NOTE: To test H0​:...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT