Question

Interested in obesity, investigators measured body mass index (BMI), a measure of weight relative to height, for both the girls and their mothers. People with high BMI are overweight. The data for 15 of the random subjects and their mothers is below: Mother BMI 23 24 21 18 26 29 25 20 24 23 22 27 28 23 21 Daughter BMI 22 24 20 21 24 27 22 21 22 21 21 25 24 20 18 The correlation between the BMI of daughters and the BMI of their mothers was r = The regression equation is y This indicates that the there is a linear relationship between the mother and daughters BMI levels. The slope indicates that as (weak, moderate, strong) postive, negative) increases by 1, the increases by when the BMI of the since our data doesn't include BMI's near zero The y-intercept predicts the BMI of the an example of For a mother with a BMI of 26, the predicted daughter BMI = Making the residual for this point is zero. This is

Answer 1

R code:

mother=c(23,24,21,18,26,29,25,20,24,23,22,27,28,23,21)
> daughter=c(22,24,20,21,24,27,22,21,22,21,21,25,24,20,18)
> length(mother)
[1] 15
> length(daughter)
[1] 15

> r=cor(mother,daughter)
> r
[1] 0.8163351

>

fit=lm(daughter~mother)
> summary(fit)

Call:
lm(formula = daughter ~ mother)

Residuals:
Min 1Q Median 3Q Max
-2.5324 -0.8032 -0.1482 0.9282 2.3148

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 7.6019 2.8736 2.645 0.020187 *  
mother 0.6157 0.1208 5.096 0.000205 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.376 on 13 degrees of freedom
Multiple R-squared: 0.6664, Adjusted R-squared: 0.6407
F-statistic: 25.97 on 1 and 13 DF, p-value: 0.0002052

• regression equation :

y = 7.6019 + 0.6157 x

• It indicates there is a strong positive linear relationship between mother and daughter BMI levels.
• The slope indicates as x increases by 1, the y increases by 0.615