Reference: MAT 2375 Introduction to statistics and MAT3378 Analysis of experience plans

Project:

Use the SAT and College GPA data set (Below)

Consider the multiple linear regression model

Y=0+1X1+2X2+3X3+4X4+

Where Y is the general average of the university.

1. high_GPA = Weighted average of grades obtained in high school

2. math_SAT = SAT score in mathematics

3. verb_SAT = Verbal note to the SAT

4. comp_GPA = Weighted average in computer science

5. univ_GPA = General average of grades obtained at university

Question:

1. Perform multiple linear regression using all predictors (independent variables) and interpret the results;

2. Test the hypohesisH0:4=0 compared toH1:4=0

3. Is the university average linearly related to the high school average?

4. Select the best model using the stepAIC function of the MASS library;

5. Compare the selected model (obtained from 3.) and the complete model (i.e. with all predictors) using adjusted R² and AIC;

6. Perform all the steps of the adequacy of the selected model.

Note: the SAT and College GPA data set

high_GPA	math_SAT	verb_SAT	comp_GPA	univ_GPA
3.45	643	589	3.76	3.52
2.78	558	512	2.87	2.91
2.52	583	503	2.54	2.4
3.67	685	602	3.83	3.47
3.24	592	538	3.29	3.47
2.1	562	486	2.64	2.37
2.82	573	548	2.86	2.4
2.36	559	536	2.03	2.24
2.42	552	583	2.81	3.02
3.51	617	591	3.41	3.32
3.48	684	649	3.61	3.59
2.14	568	592	2.48	2.54
2.59	604	582	3.21	3.19
3.46	619	624	3.52	3.71
3.51	642	619	3.41	3.58
3.68	683	642	3.52	3.4
3.91	703	684	3.84	3.73
3.72	712	652	3.64	3.49
2.15	564	501	2.14	2.25
2.48	557	549	2.21	2.37
3.09	591	584	3.17	3.29
2.71	599	562	3.01	3.19
2.46	607	619	3.17	3.28
3.32	619	558	3.01	3.37
3.61	700	721	3.72	3.61
3.82	718	732	3.78	3.81
2.64	580	538	2.51	2.4
2.19	562	507	2.1	2.21
3.34	683	648	3.21	3.58
3.48	717	724	3.68	3.51
3.56	701	714	3.48	3.62
3.81	691	684	3.71	3.6
3.92	714	706	3.81	3.65
4	689	673	3.84	3.76
2.52	554	507	2.09	2.27
2.71	564	543	2.17	2.35
3.15	668	604	2.98	3.17
3.22	691	662	3.28	3.47
2.29	573	591	2.74	3
2.03	568	517	2.19	2.74
3.14	607	624	3.28	3.37
3.52	651	683	3.68	3.54
2.91	604	583	3.17	3.28
2.83	560	542	3.17	3.39
2.65	604	617	3.31	3.28
2.41	574	548	3.07	3.19
2.54	564	500	2.38	2.52
2.66	607	528	2.94	3.08
3.21	619	573	2.84	3.01
3.34	647	608	3.17	3.42
3.68	651	683	3.72	3.6
2.84	571	543	2.17	2.4
2.74	583	510	2.42	2.83
2.71	554	538	2.49	2.38
2.24	568	519	3.38	3.21
2.48	574	602	2.07	2.24
3.14	605	619	3.22	3.4
2.83	591	584	2.71	3.07
3.44	642	608	3.31	3.52
2.89	608	573	3.28	3.47
2.67	574	538	3.19	3.08
3.24	643	607	3.24	3.38
3.29	608	649	3.53	3.41
3.87	709	688	3.72	3.64
3.94	691	645	3.98	3.71
3.42	667	583	3.09	3.01
3.52	656	609	3.42	3.37
2.24	554	542	2.07	2.34
3.29	692	563	3.17	3.29
3.41	684	672	3.51	3.4
3.56	717	649	3.49	3.38
3.61	712	708	3.51	3.28
3.28	641	608	3.4	3.31
3.21	675	632	3.38	3.42
3.48	692	698	3.54	3.39
3.62	684	609	3.48	3.51
2.92	564	591	3.09	3.17
2.81	554	509	3.14	3.2
3.11	685	694	3.28	3.41
3.28	671	609	3.41	3.29
2.7	571	503	3.02	3.17
2.62	582	591	2.97	3.12
3.72	621	589	4	3.71
3.42	651	642	3.34	3.5
3.51	673	681	3.28	3.34
3.28	651	640	3.32	3.48
3.42	672	607	3.51	3.44
3.9	591	587	3.68	3.59
3.12	582	612	3.07	3.28
2.83	609	555	2.78	3
2.09	554	480	3.68	3.42
3.17	612	590	3.3	3.41
3.28	628	580	3.34	3.49
3.02	567	602	3.17	3.28
3.42	619	623	3.07	3.17
3.06	691	683	3.19	3.24
2.76	564	549	2.15	2.34
3.19	650	684	3.11	3.28
2.23	551	554	2.17	2.29
2.48	568	541	2.14	2.08
3.76	605	590	3.74	3.64
3.49	692	683	3.27	3.42
3.07	680	692	3.19	3.25
2.19	617	503	2.98	2.76
3.46	516	528	3.28	3.41