For the attached data, find the multiple linear regression formula using X1 as the dependent variable and X2-X7 as the independent v

  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.

mlr09

X1 X2 X3 X4 X5
6.8 225 0.442 0.672 9.2
6.3 180 0.435 0.797 11.7
6.4 190 0.456 0.761 15.8
6.2 180 0.416 0.651 8.6
6.9 205 0.449 0.9 23.2
6.4 225 0.431 0.78 27.4
6.3 185 0.487 0.771 9.3
6.8 235 0.469 0.75 16
6.9 235 0.435 0.818 4.7
6.7 210 0.48 0.825 12.5
6.9 245 0.516 0.632 20.1
6.9 245 0.493 0.757 9.1
6.3 185 0.374 0.709 8.1
6.1 185 0.424 0.782 8.6
6.2 180 0.441 0.775 20.3
6.8 220 0.503 0.88 25
6.5 194 0.503 0.833 19.2
7.6 225 0.425 0.571 3.3
6.3 210 0.371 0.816 11.2
7.1 240 0.504 0.714 10.5
6.8 225 0.4 0.765 10.1
7.3 263 0.482 0.655 7.2
6.4 210 0.475 0.244 13.6
6.8 235 0.428 0.728 9
7.2 230 0.559 0.721 24.6
6.4 190 0.441 0.757 12.6
6.6 220 0.492 0.747 5.6
6.8 210 0.402 0.739 8.7
6.1 180 0.415 0.713 7.7
6.5 235 0.492 0.742 24.1
6.4 185 0.484 0.861 11.7
6 175 0.387 0.721 7.7
6 192 0.436 0.785 9.6
7.3 263 0.482 0.655 7.2
6.1 180 0.34 0.821 12.3
6.7 240 0.516 0.728 8.9
6.4 210 0.475 0.846 13.6
5.8 160 0.412 0.813 11.2
6.9 230 0.411 0.595 2.8
7 245 0.407 0.573 3.2
7.3 228 0.445 0.726 9.4
5.9 155 0.291 0.707 11.9
6.2 200 0.449 0.804 15.4
6.8 235 0.546 0.784 7.4
7 235 0.48 0.744 18.9
5.9 105 0.359 0.839 7.9
6.1 180 0.528 0.79 12.2
5.7 185 0.352 0.701 11
7.1 245 0.414 0.778 2.8
5.8 180 0.425 0.872 11.8
7.4 240 0.599 0.713 17.1
6.8 225 0.482 0.701 11.6
6.8 215 0.457 0.734 5.8
7 230 0.435 0.764 8.3

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