Question

Q1. Occupational prestige scores for a sample of fathers and their oldest son and oldest daughter are
presented below.
Family Father’s Prestige Son’s Prestige Daughter’s Prestige

A 85 82

B 78 80 77

C 75 70 68

D 70 75 77

E 69 72 60

F 66 60 52

G 64 48 48

H 52 55 57
Analyze the relationship between father’s and son’s prestige and the relationship between father’s and daughter’s prestige. For each relationship:
A. Draw a scattergram and a freehand regression line.
B. Compute the slope (b) and find the Y intercept (a).
C. State the least-squares regression line. What prestige score would you predict for a son whose
father had a prestige score of 72? What prestige score would you predict for a daughter whose
father had a prestige score of 72? D.Assume these families are a random sample and conduct a test of significance for both relationships. E.Describe the strength and direction of the relationships in a sentence or two. Does the occupational prestige of the father have an impact on his children? Does it have the same impact for daughters as it does for sons?

Answer 1

In order to solve this question I used R software.

R codes and output:

> d=read.table('data.csv',header=T,sep=',')

> head(d)

Family Father Son Daughter

1      A     85 82       NA

2      B     78 80       77

3      C     75 70       68

4      D     70 75       77

5      E     69 72       60

6      F     66 60       52

> attach(d)

The following objects are masked from d (pos = 3):

    Daughter, Family, Father, Son

> fit_1=lm(Son~Father)

> summary(fit_1)

Call:

lm(formula = Son ~ Father)

Residuals:

    Min      1Q Median      3Q     Max

-13.816 -3.154   1.509   5.176   7.124

Coefficients:

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

(Intercept)   -2.820     20.093 -0.140   0.8930

Father         1.010      0.285   3.543 0.0122 *

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7.492 on 6 degrees of freedom

Multiple R-squared: 0.6766, Adjusted R-squared: 0.6227

F-statistic: 12.55 on 1 and 6 DF, p-value: 0.01217

> plot(Father,Son)

> abline(fit_1)

> fit_2=lm(Daughter~Father)

> summary(fit_2)

Call:

lm(formula = Daughter ~ Father)

Residuals:

      2       3       4       5       6       7       8

5.246 -1.118 12.277 -3.844 -9.208 -11.450   8.097

Coefficients:

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

(Intercept)   3.1996    32.0851   0.100    0.924

Father        0.8789     0.4707   1.867    0.121

Residual standard error: 9.754 on 5 degrees of freedom

Multiple R-squared: 0.4108, Adjusted R-squared: 0.293

F-statistic: 3.487 on 1 and 5 DF, p-value: 0.1208

> plot(Father,Daughter)

> abline(fit_2)

Que.a

Scatter plot for father and son:

Mo 80 75 70 Son 65 60 55 o 50 55 60 65 70 75 80 85 Father

Scatter plot for father and daughter:

o 75 70 65 Daughter O 60 O 55 50 55 60 65 70 75 80 85 Father

B.

For son:

Slope = 1.01. and intercept = -2.82

For daughter:
Slope = 0.8789. and intercept = 3.1996

Que.c

Regression equation for son:

Son = -2.82 + 1.01 Father

Prestige score for son when father's prestige score = 72 is

Son = -2.82 + 1.01 Father

Son = -2.82 + 1.01 (72)

Son = 69.9

Regression equation for daughter:

Daughter = 3.1996 + 0.8789  Father

Prestige score for daughter when father's prestige score = 72 is

Daughter = 3.1996 + 0.8789  Father

Daughter = 3.1996 + 0.8789  (72)

Daughter = 66.4804

Que. D

For son:

P-value for testing significance of slope coefficient is 0.0122, which is less than 0.05, hence this model is statistically significant.

For Daughter:

P-value for testing significance of slope coefficient is 0.121, which is greater than 0.05, hence this model is not statistically significant.

Que.e

> cor(Father, Son)

[1] 0.8225655
We see that there is high degree positive relation between father's prestige and son's prestige.  

Also relation between father's prestige and daughter's prestige is positive. However in above part we see that it is not statistically significant.

Hence we see that occupational prestige of the father does not have an impact on his son's prestige and daughter's prestige.