multiple regression analysis

1. For the attached data, find the multiple linear regression formula using X1 as the dependent variable and X2-X7 as the independent variables.
2. Using whatever means necessary find the model of best fit and justify your choices.
3. Determine what variables are significant at a sig. level of 10%.  
4. State what independent variable if any should be tested for interaction.
5. Choose any two observed variables and calculate their residuals.
6. What are the 4 assumptions about the error terms, (residuals) that need to be in order to perform multiple linear regression.

mlr0

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9

.8

42

2

7

.7

180

6.4

6.3

7

16

6.9 235 0.435

0.48

6.9

6.9 245

6.3 185

185

8.6

6.2 180

6.8

25

0.503

225

6.3 210

6.8 225 0.4

6.4 210

6.8 235

9

7.2

6.4 190 0.441 0.757

220

6.8 210

6.1 180

6.5 235 0.492

6.4 185

11.7

6

0.721 7.7

6

7.3 263 0.482 0.655 7.2

6.1 180

6.7 240 0.516 0.728

6.4 210 0.475

13.6

5.8

11.2

6.9 230

7 245

3.2

7.3

6.2

0.449

6.8 235

7.4

7 235 0.48

5.9

6.1 180

0.79

185

11

7.1 245

2.8

5.8 180 0.425

7.4 240

0.713

6.8 225 0.482 0.701

6.8

5.8

7 230 0.435

X1	X2	X3	X4	X5
							6		2	25		0.4	0.6			7	9.2
			6.3							180			0.435		0.79			11
					6.4		190	0.456	0.761	1			5.8
		6.2	0.4	16	0.651		8.6
				6.9	205		0.449	0.9	2	3.2
		225	0.431	0.78	2		7.4
				185			0.48	0.771	9.3
		6.8						235	0.469	0.75
0.818	4.7
	6.7					210	0.825	12.5
			245		0.516	0.632	20.1
0.493		0.757	9.1
0.374	0.709	8.1
			6.1	0.424	0.782
	0.441	0.775	20.3
	220		0.503	0.88
	6.5	194	0.833	19.2
7.6		0.425	0.571	3.3
0.371	0.816		11.2
	7.1			240	0.504	0.714	10.5
0.765	10.1
		7.3		263			0.482		0.655			7.2
	0.475	0.244		13.6
0.428		0.728
		230	0.559		0.721	24.6
12.6
6.6		0.492	0.747	5.6
0.402	0.739	8.7
0.415		0.713		7.7
0.742	24.1
0.484	0.861
175	0.387
192	0.436	0.785	9.6
0.34	0.821	12.3
8.9
0.846
160	0.412	0.813
0.411	0.595		2.8
0.407	0.573
228	0.445	0.726	9.4
	5.9	155	0.291	0.707	11.9
200	0.804	15.4
0.546	0.784
0.744	18.9
105	0.359	0.839	7.9
0.528	12.2
5.7	0.352		0.701
0.414	0.778
0.872	11.8
0.599	17.1
11.6
215	0.457	0.734
0.764	8.3