Question

One of the characteristics is an index of the professor's "beauty" as rated by a panel of six judges. In this exercise, you will investigate how course evaluations are related to the professor's beauty.

The following table uses data on course evaluations, course characteristics, and professor characteristics for 463 courses at the University of Texas at Austin. Use a statistical package of your choice to answer the following questions.

Suppose you are interested in estimating the following model

Course Evaluation = beta 0β0 + beta 1β1Beauty + u

Run a regression of average course evaluation (Course Evaluation ) on the professor's beauty (Beauty ).

What is the estimated intercept β̂0 ?

What is the estimated slope β̂1?

The estimated model is Course Evaluation = ?

Where the number in parentheses is the homoskedastic standard error for the regression coefficient β̂1.

Suppose you wanted to test the hypothesis that β̂1 equals zero at the 1%, 5% and 10% level. That is, H0 : β1 vs. H1: β1 ≠ 0 Report the

t -statistic and p -value for this test.

Can you reject the null hypothesis at the 5% significance level? (Yes/No)

Teaching Ratings
CourseEval	Beauty
4.93	-0.48522
4.85	0.01629
3.5	-0.15495
4.22	-1.2598
4.77	0.72995
5.2	0.65696
3	-0.37775
4.11	-0.18491
3.61	0.03973
4.17	0.94806
3.03	1.15703
3.9	0.1805
2.87	-0.38551
3	0.10505
2.07	0.46896
4.48	-0.28626
4.94	-0.98913
2.95	0.85618
4.67	-0.42774
4.03	-0.53527
4.17	0.05048
3.94	-1.58871
4.24	-0.12336
5.31	0.08465
4.14	1.13106
3.87	0.33073
4.37	0.05321
3.85	-0.91025
3.92	-0.73834
2.34	0.53985
2.96	-0.24181
4.16	-1.64258
3.9	1.34169
3.69	-0.71292
5.13	-1.06732
3.27	1.86866
4.22	-0.23998
4.73	-0.11554
4.62	-0.5808
2.82	0.74568
4.16	-0.47213
3.43	1.05884
2.81	1.9106
3	1.34707
4.65	-0.38525
3.96	1.20135
3.89	-0.02092
2.75	0.46187
3.67	0.04074
4.8	-0.18052
4.39	-0.20429
5.03	-0.07543
4.15	1.26501
3.37	-2.42455
3.44	1.37851
4.16	-0.66968
3.78	1.86713
4.25	-1.531
3.58	-1.23474
3.8	-0.13042
3.12	-0.28536
4.43	-0.26543
3.1	-0.14884
3.66	1.88186
4.22	-1.42136
4.25	-0.66971
4	2.27531
1.86	-2.40699
2.23	0.85439
4.48	-0.69331
4.56	-1.07374
4.42	0.7688
4.16	1.09661
4.42	-1.00051
3.78	-0.3075
2.72	0.16203
5.02	-1.06189
3.45	-0.0882
4.8	-0.04489
4.83	1.96868
4.92	-0.99902
2.98	-1.37009
4.23	0.32778
3.45	2.15386
4.32	1.68281
5.37	2.63759
3.48	0.14337
2.95	-0.21691
3.68	1.04247
3.26	0.20289
4.56	0.06961
2.94	0.19544
4.5	1.30034
2.93	-0.33539
3.28	0.02444
4.55	-0.17583
4.65	-0.34484
3.84	-0.68216
2.62	0.07549
2.71	1.24529

Answer 1

Solution:

The below output can be found by use of excel data analysis tool, the steps are given below.

1) Select the data tab at the ribbon and the data analysis tool.

2)Click on regression in the list.

3) Select Y range and X range and alpha level, and output range.

The intercept and slope coefficient is in yellow highlighted cells, and t statistics in blue cell and the p-value is in the orange cell. Since the p-value is greater than all level of significance therefore, we reject the null hypothesis and slope coefficient is different from 0.