Use the following to answer questions 20 through 24. A multiple linear regressio

Question

Use the following to answer questions 20 through 24. A multiple linear regression model is used to predict the mid-upper arm circumference (MUAC) of Ethiopian teenagers. The explanatory variables in the model are height (cm) and househould income, measured in Ethiopian currency (the birr).

Residuals:

Min    1Q Median 3Q Max

-5.188 -1.851 -0.012 1.581 5.796

Coefficients:

Estimate    Std. Error    t value    Pr(>|t|)

(Intercept) 6.884958 5.713208 1.205    0.23420

height_cm 0.101084    0.036811    2.746    0.00852

hhincome -0.000730 0.001388    -0.526    0.60142

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Residual standard error: 2.459 on 47 degrees of freedom Multiple R-squared: 0.1397,Adjusted R-squared: 0.1031 F-statistic: 3.817 on 2 and 47 DF, p-value: 0.0291

20. What is the estimated linear regression equation?

a. yˆ = 6.8849 + 0.1010 × height cm ? 0.0007 × hhincome

b. yˆ = 6.8849 + 0.1010 × hhincome ? 0.0007 × height cm

c. yˆ = 6.8849 × MUAC + 0.1010 × height cm ? 0.0007 × hhincome

d. yˆ = 6.8849 × MUAC + 5.7132 × height cm + 1.205 × hhincome

e. none of the above

21. Which of the following statements is true?

a. Because two out of the three p-values are greater than 0.05 we have evidence that the observations in the data set are not independent.

b. The model output indicates that the distribution of the residuals is left-skewed.

c. The interpretation of the slope associated with height cm is that as height increases by 0.1 centimeter, hhincome decrease by 0.0007 birr.

d. Because the p-value associated with hhincome is greater than 0.05 we have evidence that there is a nonlinear association between hhincome and MUAC.

e. None of the above are true.

22. What is the null hypothesis tested on the line where the p-value is 0.00852?

a. H0: ?0 = 0

b. H0: ?1 = 0

c. H0: ?2 = 0

d. H0: ?ˆ 1 = 1

e. H0: ?ˆ 1 = 0 9

23. How many individuals were included in this analysis?

a. 47

b. 48

c. 49

d. 50

e. 51

24. How would you calculate a 95% confidence interval for the intercept?

a. 6.88 ± 1.21 × 5.71

b. 6.88 ± 2.01 × 5.71

c. 6.88 ± 1.96 × 5.71

d. 5.71 ± 1.21 × 0.23

e. 5.71 ± 1.96 × 0.23

Explanation / Answer

Answer 20

Independent variables are heigth and hhincome, so only height and hhincome will be on the right hand side of the regression equation

Dependent variable is MUAC, so only MUAC will be there on the left hand side of the regression

We know regression equation for two independent variables looks like

y = a + b1x1 + b2x2

here x1 = height, b1 = 0.101084, x2 = hhincome, b2= -0.00073 and a= 6.8849

here a is intercept and we got the value of a, b1 and b2 from the output data given in the question

so, the regression equation becomes

y^ = 6.8849 + 0.1010*height -0.0007*hhincome

Only option A is correct

option C and D are incorrect because these options have MUAC on the right hand of equation which is incorrect representation of regression equation

ooption B is incorrect because the coefficient of height and hhincome are interchanged in the regression equation

so, option A is only correct answer

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