Heights of mothers and daughters 2.4.1. For the heights data in the file heights

Question

Heights of mothers and daughters 2.4.1. For the heights data in the file heights.txt, compute the regres sion of Dheight on Mheight, and report the estimates, their standard errors, the value of the coefficient of determination, and the esti mate of variance. Give the analysis of variance table that tests the hypothesis that E(DheightMheight) = A) versus the alternative that E(Dh eightMheight) = 0 + 1Mheight, and write a sentence or two that summarize s the results of these computations. 2.4.2. Write the mean function in the deviations from the mean form as in Problem 2.3. For this particular problem, give an interpretation for the value of A. In particular, discuss the three cases of | = 1, A 1 . Obtain a 99% confidence interval for ! from the data. 2.4.3. Obtain a prediction and 99% prediction interval for a daughter whose mother is 64 inches a

Explanation / Answer

2.4.1

R - Command

> Heights <- read.csv("~/Desktop/Heights.csv")
> View(Heights)
> attach(Heights)
> mod1 <- lm(Dheight ~ Mheight)
> summary(mod1)

R - output

Call:
lm(formula = Dheight ~ Mheight)

Residuals:
Min 1Q Median 3Q Max
-7.397 -1.529 0.036 1.492 9.053

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 29.91744 1.62247 18.44 <2e-16 ***
Mheight 0.54175 0.02596 20.87 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.266 on 1373 degrees of freedom
Multiple R-squared: 0.2408,   Adjusted R-squared: 0.2402
F-statistic: 435.5 on 1 and 1373 DF, p-value: < 2.2e-16

R - command for ANOVA

> ANOVA1 = aov(Mheight ~ Dheight)
> summary(ANOVA1)
Df Sum Sq Mean Sq F value Pr(>F)
Dheight 1 1835 1835.1 435.5 <2e-16 ***
Residuals 1373 5786 4.2   
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Conclusion of Test

Since value of F-statistics is very high, we have suficient evidence to reject H0 : b1 = 0. So, estimated value of slope parameter 0.54175 can be used for regression.

FOR 2.4.2, question has asked for reference of Q2.3

Slope Parameter = 1 implies expected "daughter height" is same as "mother height".

Slope Parameter < 1 implies expected "daughter height" will be less than "mother height".

Slope Parameter > 1 implies expected "daughter height" will be more than "mother height".

> confint(mod1, 'Mheight', level = 0.99)
0.5 % 99.5 %
Mheight 0.4747836 0.6087104

99% CI of slope parameter (0.4747836, 0.608710)

Conclusion : Expected Daughter height will be less mother height.

2.4.3

> newdata = data.frame(Mheight = 64)

> predict(mod1, newdata, interval= "predict", level = 0.99)
fit lwr upr
1 64.58925 58.74045 70.43805

Predcited Height = 64.58925

99% Confidence Interval = (58.74045, 70.43805)

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.