A) Create a model to predict % body fat from weight. Choose the correct formula

Question

A) Create a model to predict % body fat from weight. Choose the correct formula for the regression line below. B) Do you think a linear model is appropriate? Explain C) Interpret the slope of your model D) Is your model likely to make reliable estimates? Explain E) What is the residual for a person who weighs 203 pounds and has a 19.2% body fat? Question Help * Researchers hoping to find ways to make a good estimate of a person's body fat percentage without immersing him or her in water, immersed 15 male subjects and recorded ther weights, Use the data to answer the questions below Weight (b) 171 175 176.176 176 183 184 189 197 205 210211212213227 %Body Fat25 24 24 31 26 26 28 29 36 32 29 35 35 31 30 a) Create a model to predict %body fat from weight Choose the correct formula fr the regression line below O A. y-0703x+0.148 OB. y 0 703+0.148x O C.0.703y+0.148 O D. 0703+0.148y b) Do you think a linear model is appropriate? Explain. A. The fit is not good enough The linear model is not appropriate O B. The residuats plot shows no apparent pattern. The linear model is appropriata C. The regression has R2 45 2% The linear model is approprate 0 D. The standard devabon of the residuals s 3 174 The Inear c) Interpret the slope of your model model is appropriate A. For each additional pound of weght body fat increases by 0 703% O B. For each addition, pound of weght body fat ncreases by 0 148% O C. For each additional 1% body fat, weight ncreases by O 703 pounds Click to select your answer(s)

Explanation / Answer

Sol:

Take x as weight

y as % bodyfat

perform regression in excel.

solutionb:

RESIDUAL PLOT SHOWS NO APPARENT PATTERN LINEAR MODEL IS APPROPRIATE.

Solutionc:

m=slope=change in y/change in x

0.148=change in % bodyfat/% change in weight

intrepretation:

For each additional pound of weight ,body fat increases by 0.148%

y hat=0.703+0.148x

% body fat=0.703+0.148 weight

slope=0.148

y intercept=0.703

OPTION B

SUMMARY OUTPUT Regression Statistics Multiple R 0.671829 R Square 0.451354 Adjusted R Square 0.409151 Standard Error 3.058153 Observations 15 ANOVA df SS MS F Significance F Regression 1 100.0201 100.0201 10.69471 0.006086 Residual 13 121.5799 9.352298 Total 14 221.6 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Intercept 0.702868 8.810592 0.079775 0.937631 -18.3313 19.737 -18.3313 weight 0.148178 0.045311 3.270277 0.006086 0.050291 0.246065 0.050291

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