Question

Question Type 1 The following data sets each contain 3 random observations of two variables. For each data set, answer the following questions: Question (a) The data below is a random sample of 3 observations drawn from the United States population. Use the data to answer the following questions i. Find 95% confidence intervals of the population mean of experience and wage ii. Estimate pe,w, the correlation between the variables experience and wage. iii. Find Bı and Po, the estimates of the parameters in the following regression equation wage = β0 + β|education + € iv. Predict wages for a person with 15 years of edcuation using your regression estimate. v. Find the R2 wage education 16.20 12.36 14.40 12.00 12 13 12 12

Question 1

Answer 1

#code in R

wage <- c(16.20,12.36,14.4,12)
educ <- c(13,13,12,12)
t.test(wage,mu=15)
t.test(educ,mu = 12)
cor(wage,educ)
model <- lm(wage~educ)
summary(model)
predict(model,data.frame(educ=15))

#running the code

> wage <- c(16.20,12.36,14.4,12)
> educ <- c(13,13,12,12)
> t.test(wage,mu=15)

        One Sample t-test

data:  wage
t = -1.2916, df = 3, p-value = 0.287
alternative hypothesis: true mean is not equal to 15
95 percent confidence interval:
 10.63552 16.84448
sample estimates:
mean of x 
    13.74 

> t.test(educ,mu = 12)

        One Sample t-test

data:  educ
t = 1.7321, df = 3, p-value = 0.1817
alternative hypothesis: true mean is not equal to 12
95 percent confidence interval:
 11.58131 13.41869
sample estimates:
mean of x 
     12.5 

> cor(wage,educ)
[1] 0.3195994
> model <- lm(wage~educ)
> summary(model)

Call:
lm(formula = wage ~ educ)

Residuals:
    1     2     3     4 
 1.92 -1.92  1.20 -1.20 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)    0.240     28.325   0.008    0.994
educ           1.080      2.264   0.477    0.680

Residual standard error: 2.264 on 2 degrees of freedom
Multiple R-squared:  0.1021,    Adjusted R-squared:  -0.3468 
F-statistic: 0.2275 on 1 and 2 DF,  p-value: 0.6804

> predict(model,data.frame(educ=15))
    1 
16.44 

i)

95% confidence interval for wage =

 10.63552 16.84448

95% confidence interval for education =

11.58131 13.41869

ii)

correlation =

0.3195994

iii)

b0 = 0.24

b1 = 1.08

y^ = 0.240 + 1.08 x

iv)

16.44 

v)

R^2 = 0.1021