6. The following data were obtained from a sample of 12 respondents. With respon

Question

6. The following data were obtained from a sample of 12 respondents. With respondents' highest grade of schooling completed as your dependent variable and fathers' highest grade of schooling completed as your independent variable, calculate the Y-intercept and the slope and write down the linear regression equation which summarizes the relationship between these two variables Highest Grade of School Highest Grade of School Highest Grade of School Completed (Respondent) 12 14 14 10 14 16 15 12 16 14 15 14 Completed (Father) 12 10 14 8 12 12 10 Completed (Mother) 12 12 12 8 12 12 16 13 14 14 20 13 12 14 Mean St. Dev Variance 13.83 1.75 3.06 11.75 2.90 8.02 11.50 3.90 15.18

Explanation / Answer

We solve above equation in R software

we put the programm in r

Y=c(12,14,14,10,14,16,15,12,16,14,15,14) ### dependent variable
X=c(12,10,14,8,12,12,10,6,16,13,14,14) ### independent variable
fit=lm(Y~X) ### fitting regression model
fit
summary(fit) ### summary of regression equation

We get the out put of above programm is,

> Y=c(12,14,14,10,14,16,15,12,16,14,15,14) ### dependent variable
> X=c(12,10,14,8,12,12,10,6,16,13,14,14) ### independent variable
> fit=lm(Y~X) ### fitting regression model
> fit

Call:
lm(formula = Y ~ X)

Coefficients:
(Intercept) X  
9.1067 0.4023  

> summary(fit) ### summary of regression equation

Call:
lm(formula = Y ~ X)

Residuals:
Min 1Q Median 3Q Max
-2.3248 -0.7384 0.1638 0.5774 2.0661

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 9.1067 1.7873 5.095 0.000467 ***
X 0.4023 0.1482 2.714 0.021780 *  
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.392 on 10 degrees of freedom
Multiple R-squared: 0.4242, Adjusted R-squared: 0.3666
F-statistic: 7.366 on 1 and 10 DF, p-value: 0.02178

here Y- intercept is  9.1067

and Slope is 0.4023

linear euation is,

Y=9.1067+0.4023X

_______________________________________________________-***________________________------------------

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

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