A chemical engineer is interested in the weightloss(in pounds) of a particular c

Question

A chemical engineer is interested in the weightloss(in pounds) of a particular compound as a function of the time(in hours) the compound is exposed to air. The R ouput and scatterplot are given below. (10pts) lm(formula = data1$Weightloss ~ data1$Exposuretime) Residuals: Min 1Q Median 3Q Max -1.5333 -0.5625 0.3917 0.5458 0.7667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -1.7333 1.1652 -1.488 0.168 data1$Exposuretime 1.3167 0.2076 6.342 8.44e-05 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.8041 on 10 degrees of freedom Multiple R-squared: 0.8009, Adjusted R-squared: 0.781 F-statistic: 40.22 on 1 and 10 DF, p-value: 8.437e-05 1. What are the independent and dependent variables? 2. What is the estimate for intercept, 0 and slope, 1? Interpret both. 3. Write down the estimated model? 4. What is the coefficient of determination, R2, interpret this. 5. Test the hypothesis H0: 1=0 vs. H1: 1 0? Based on your testing result, what is your conclusion (use =0.01)? 6. Check the residual plot and comment if a linear model is appropriate. 7. Use the Q-Q plot and comment if the residuals are normally distributed. 8. Comment on the overall appropriateness of the model.

Explanation / Answer

1. Independent random variable is Exposuretime

Dependent Variable = Weightloss

2. Intercept = -1.7333

  data1$Exposuretime = 1.3167

If one dollar increase in expouretime then Weightloss also increase 1.3167 dollars

and vice versa, since Slope = 1.3167 is greater than 0, So it is poistive correlation

3. Residual standard error: 0.8041

4. Multiple R-squared: 0.8009 = 80.09 % of variations in the variable exposuretime is explained by using independent variable weightloss.

5. P-value =  8.44e-05 < alpha 0.01, so we reject H0

Thus, we conclude that population regression coefficieint is not equal to Zero i.e. 1 0

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.