[Solved]R Programming Dataset Package Cement Company Wants Understand Heat Evolved Setting Cement Q37112894

R programming Dataset in package

A cement company wants to understand the heat evolved in settingof their cement product as a function of proportion of four mainchemical ingredients to come up with a better design. Suppose theyhire you as a statistician and provide you with their dataset whichyou can find in the MASS package under the name

‘cement’.

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1) Using simple regression models, which one of the 4 chemicalingredients, is able to explain the most variation in the heatevolved (y)?

a) X1

b) X2

c) X3

d) X4

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2) Using simple regression models, which one of the 4 chemicalingredients, is able to explain the least variation in the heatevolved?

a) X1

b) X2

c) X3

d) X4

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3) Consider the model with the ingredient found in Question 6 asthe base model. Add the ingredient which performs second-best asper Question 6. Now what happens to the in the new model as compared to the best model?

a) It decreases by about 4.5%

b) It decrease by about 10%

c) It increases by about 4.5%

d) It increases by about 10%

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4) Consider the three conclusions that can be drawn from youranswer in Q.8.

(i). The RAdjusted2 decreases as the new variable is adding very little newinformation about the response to the base model.

(ii). The RAdjusted2 decreases as the new variable is correlated with thevariable already present in the base model. (What is the VIF of thenew model? How much is the correlation between the two variablespresent in the model?)

(iii). The RAdjusted2 increases as the new variable is adding significantinformation to the base model.

Which of the above two are correct conclusions?

a) Only i

b) Only ii

c) Both i and ii

d) Only iii

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5) Consider the new model you developed in Q.8. What do youconclude about the statistical significance of the model (atsignificance level of 5%) you developed.

a) The model is statistically significant as the F-statistic islarger than the critical value and the corresponding p-value islower than 0.05.

b) The model is not statistically significant as the F-statisticis lower than the critical value the corresponding p-value islarger than 0.05.

c) The model is not statistically significant as the Adjusted R2is smaller than the Adjusted R2 of the base model.

d) The model is statistically significant as the Adjusted R2 islarger than the Adjusted R2 of the base model.

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