Problem 6.10.2 You will need this data: https://drive.google.com/file/d/1y1HTWeV
ID: 3358363 • Letter: P
Question
Problem 6.10.2
You will need this data: https://drive.google.com/file/d/1y1HTWeVcxdzZxFr0Za9oPOM2SxAEgLHS/view
and read problem 6.10.1
You will need to use R, Stata, Mathlab etc.
Thank you
Compute and summarize the following three hypulM NII: .-) vs. Al l: .o NH: .-/, = , = () vs. All: Not all 0 ratings data introduced in Problem 1.6, suppose we were interested modeling the quality rating. We take as potential predictors character 6.10 RateMyProfessor.com (Data file: Rateprof) In the pro professor, the number of istics of the instructor, including gender of the years numYears in which the instructor had ratings, between 1 2009, a factor discipline, with levels for humanities, social sci pre-professional, and stem for science technology, engineering, and ma ematics Additional potential predictors are easiness, average rati of the easiness of the course, raterInterest in the course material final predictor is pepper, a factor with levels no and yes. A value yes means that the consensus is that the instructor is physically attrac tive. The variables helpfulness and clarity have been excluded since these are essentially the same as quality (Section 5.5). Data are ence, included for n 366 professors 6.10.1 Fit the first-order regression model quality-gender+ numYears + pepper + discipline +easiness raterInterest, and print the summary table of coefficient estimates. Suppose that p, is the coefficient for numYears. level for the following three hypothesis a test and significance l tests: (1) NH : = 0 versus AH : A0; (2) NH : A =0 versus AH : $0; (1) NH : = 0 versus AH : 2 0. 6.10.2 Obtain the Type II analysis of variance table. Verify th F-tests in the table are the squares of the t-tests in the coefficient table, with the exception of the tests for the regressors for discipline. Summarize the resultsoExplanation / Answer
> data1=read.csv(file.choose(),header=T)
> attach(data1)
> model=lm(quality~gender+numYears+pepper+discipline+easiness+raterInterest)
> summary(model)
Call:
lm(formula = quality ~ gender + numYears + pepper + discipline +
easiness + raterInterest)
Residuals:
Min 1Q Median 3Q Max
-1.31272 -0.47727 0.07188 0.46867 1.15673
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.10322 0.38851 -0.266 0.791
gendermale 0.07728 0.11470 0.674 0.502
numYears 0.01283 0.01770 0.725 0.470
pepperyes 0.23344 0.19886 1.174 0.243
disciplineSTEM 0.05016 0.11737 0.427 0.670
easiness 0.49347 0.07565 6.523 2.17e-09 ***
raterInterest 0.59076 0.09808 6.023 2.31e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.602 on 110 degrees of freedom
Multiple R-squared: 0.5279, Adjusted R-squared: 0.5021
F-statistic: 20.5 on 6 and 110 DF, p-value: 5.434e-16
1) t-test :p-value = 0.470.
Since p-value < 0.05, we reject the null hypothesis of no significance and conclude that numYears has a significant effect on the quality variable.
2) t-test : t-stat = 0.725
p-value = P[t110< 0.725] = 0.7650043
Since p-value > 0.05, we accept the null hypothesis and conclude that numYears has no significant effect on the quality variable.
3)t-test : t-stat = 0.725
p-value = P[t110> 0.725] = 0.2349957.
Since p-value < 0.05, we reject the null hypothesis and conclude that numYears has a significant effect on the quality variable.