Question

We continue with the Concrete dataset. Concrete is a central product for most modern constructions and is used in homes, roads, and commercial structures and there are many other building applications. Frequently, there is an issue of strength (compressive strength) which is measured in megapascals (MPa). Several attributes contribute to the strength of concrete.

1. Download the data file https://docs.google.com/spreadsheets/d/1jVV26-UbjWhGEOi9Aww81JmSj3kM3JY6lQY662VK-pg/edit?usp=sharing

2. Run a multiple regression predicting the strength of the concrete based on Cement, Blast Furnace Slag, Fly Ash, Water, Superplasticizer, Course Aggregate, Fine Aggregate, and Age.

3. Then move forward in the assignment answering the questions that follow.

How much correlation is there between the variables?

How much of the variability in strength is explained by the predictors?

The deviation between the R² and R²_adj is severe? True or False

Which of the predictor variables are significant at the 0.05 level?

At the 0.05 level of significance, what is the conclusion about the overall model hypothesis test?

What is the 90% confidence interval around the ? for water?

Answer 1

2)

3)

How much correlation is there between the variables?

r = sqrt(R^2) = sqrt(.61551987) = 0.78455

How much of the variability in strength is explained by the predictors?

The coefficient of determination tells the percentage of variation in strength which is explained by all independent variables in the model. The coefficient of determination, R square, in this case, is 61.55%.

The deviation between the R² and R²_adj is severe? True or False

The coefficient of determination, R^2 = 61.55%

The Adjusted R square, R^2(adj) = 61.25%

health statement of severe deviation between R^2 and R^2(Adj) is false.

Which of the predictor variables are significant at the 0.05 level?

Ho: Xi is not a significant predictor of strength, beta_i = 0

V/s h1: Xi is a significant predictor of strength, beta_i =/= 0

With p-value<5%, I can say that Cement, Blast Furnace Slag, Fly Ash, Water, Superplasticizer, Age (day) are significant predictor of strength

At the 0.05 level of significance, what is the conclusion about the overall model hypothesis test?

Ho: model is not significant. v/s h1: model is significant. with (F=204.31, P<5%), I REJECT ho and conclude that the model is significant.

What is the 90% confidence interval around the? For water?

CI of slope = beta4 +- t(A/2,n-1)*SE_beta4

lower =-0.1499-3.73144*0.040177 = -0.299818065
upper =-0.1499+3.73144*0.040177 = 1.80649E-05