A study was done on a diesel-powered light-duty pickup truck to see if humidity, air temperature, and barometric pressure influence emission of nitrous oxide (in ppm). Emission measurements were taken at different times, with varying experimental conditions. The data are given in Table below.

Nitrous oxide, Y	Humidity, X1	Temperature, X2	Barometric Pressure, X3
0.9	72.4	76.3	29.18
0.91	41.6	70.3	29.35
0.96	34.3	77.1	29.24
0.89	35.1	68	29.27
1	10.7	79	29.78
1.1	12.9	67.4	29.39
1.15	8.3	66.8	29.69
1.03	20.1	76.9	29.48
0.77	72.2	77.7	29.09
1.07	24	67.7	29.6
1.07	23.2	76.8	29.38
0.94	47.4	86.6	29.35
1.1	31.5	76.9	29.63
1.1	10.6	86.3	29.56
1.1	11.2	86	29.48
0.91	73.3	76.3	29.4
0.87	75.4	77.9	29.28
0.78	96.6	78.7	29.29
0.82	107.4	86.8	29.03
0.95	54.9	70.9	29.37

1. Construct the correlation matrix for the variables in Table. Interpret the correlations in the matrix.
2. Fit this multiple linear regression model to the given data and then estimate the amount of nitrous oxide emitted for the conditions where humidity is 50%, temperature is 76◦F, and barometric pressure is 29.30.
3. Discuss the accuracy of the forecast made in part b, and the importance of each independent variable. By calculating sum of squares decomposition and associated degrees of freedom, Standard error of the estimate, F statistic for testing the significance of the regression.
4. Compute the variance inflation factors (VIFs) for the independent variables. Is multicollinearity a problem for these data? If so, how might you modify the regression model?
5. Compute the ‘Best Subsets Regression,’ decide for the best model and find the nitrous oxide emitted.

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