The following data are the monthly salaries y and the grade point averages x for

Question

The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration. GPA Monthly Salary ($) 2.7 3,600 3.4 3,800 3.7 4,300 3.2 3,700 3.5 4,100 2.7 2,400 The estimated regression equation for these data is y^cap = -495.5 + 1,295.5x and MSE = 184,545. a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal). $ _____ b. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA (to 2 decimals) S(______, ______) c. Develop a 95% prediction interval for Ryan Dailey, a student with a GPA of 3.0 (to 2 decimals). $(______,______)

Explanation / Answer

a) The regression equation is Y = -495.5 +1295.5*x , so put x = 3

-495.5 +1295.5*3 = 3391

b)

We shall use R , open source statistical package to answer the questions

# read the data into R dataframe
data.df<- read.csv("C:\Users\586645\Downloads\Chegg\sal.csv",header=TRUE)
str(data.df)

# perform anova analysis
fit<- lm(sal~ gpa,data=data.df)

#summarise the results
summary(fit)

attach(data.df)
confint(fit, 'gpa', level=0.95)

newdata <- data.frame(gpa = 3, sal= 3391)
predict(fit, newdata, interval="predict")

The results are

95% confidence interval are

> confint(fit, 'gpa', level=0.95)
2.5 % 97.5 %
gpa 24.00412 2566.905

prediction interval

> predict(fit, newdata, interval="predict")
fit lwr upr
1 3390.909 2077.761 4704.057

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