Use Data Set 1 on p. 766 - 767 and answer the following questions. 1. Choose and

Question

Use Data Set 1 on p. 766 - 767 and answer the following questions. 1. Choose and state one of the given columns as your explanatory (independent) variable. 2. Choose and state one of the given columns as your response (dependent) variable. 3. Find the linear regression equation for the columns you chose. Use any 30 pieces of data. 4. Check the resulting correlation coefficient against Table A-6 with a significance level of 0.05 and determine if there is linear correlation. Show your work and results. 5. Use the results of #3 and #4 to predict the value of the response variable for a value of the explanatory variable not given in its column. State what value you use for the | explanatory variable and show your work to find the value for the response variable. 6. Write a concluding sentence summarizing the solution for #5. Include the values with units for the explanatory and response variables and why you think this is the best predictor.

Explanation / Answer

Consider dependent variable is weight (WT) and independent variable is HT

We can fit regression in MINITAB.

steps :

ENTER data into MINITAB sheet --> Stat --> Regression --> regression --> Response : WT --> Predictors : HT--> Results : select second option --> ok --> ok

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Regression Analysis: WT versus HT

The regression equation is
WT = - 101 + 3.99 HT

Predictor Coef SE Coef T P
Constant -101.24 98.09 -1.03 0.311
HT 3.986 1.436 2.78 0.010

S = 23.12 R-Sq = 21.6% R-Sq(adj) = 18.8%

Analysis of Variance

Source DF SS MS F P
Regression 1 4115.2 4115.2 7.70 0.010
Residual Error 28 14962.7 534.4
Total 29 19077.9

Here we have to test,

H0 : Rho = 0 Vs zh1 : Rho not= 0

where Rho is population correlation between weight and height.

Assume alpha = level of significance = 0.05

Test statistic follows t-distribution with n-2 degrees of freedom.

From the given output,

T = 2.78 for HT

p-value = 0.010

P-value < alpha

Reject H0 at 5% level of significance.

COnclusion : There is sufficient evidence to say that there is some relationship between WT and HT.

Now consider HT = 63.8 and find WT.

This we can find by using regression equation.

WT = - 101 + 3.99 HT

WT = -101 + 3.99*63.8 = 153.56

The predicted value of Wt when HT = 63.8 is 153.56

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