# solve the relevant problems given in your research data

objective: You have to show that you are able to use linear regression techniques and interpret the results that you obtain, such as coefficient estimates, r-squared, adjusted r-squared, ANOVA table, p-value, standard error, etc.

Please use the â€œconcrete_trainâ€ dataset to fit a regression model. Make sure that you:

• Interpret your findings (coefficient estimates, r-squared, adjusted r-squared, ANOVA table, p-value, standard error, etc.)
• Perform variable selection (backward)
• Make model comparison using the proper metric (it might be r-squared or adjusted r-squared but justify why you use one over the other)
• Check the correlation matrix (and comment on it)
• Run regression diagnostic (to see any transformation is needed or any assumption is violated)

After deciding on the best model (it may vary from person to person), use that regression model to predict the strength of the concrete in â€œconcrete_testâ€ dataset. Then, please upload the predictions to the canvas so that I can evaluate how good the predictions are.

Data source

The data, collected by Yeh, consists of 1030 observations with 9 quantitative variables: cement, age, blast furnace slag, fly ash, water, superplasticizer, coarse aggregate, fine aggregate, and compressive strength. The description of each of these variables is given in Table 1. Note that I split the data into two parts â€“ train set (803 observations) and test set (200 observations). Therefore, you are going to work with the training dataset to create a regression model and use it to predict the strength of the concretes in the “concrete_test” data.

Table 2. Definition of variables

 Variable name Definition Cement ASTM type I, Portland Cement Slag Supplied by a local steel plant in Taiwan Fly Ash Manufactured as a byproduct by a power plant Water Normal Tap water Superplasticizer ASTM C494 type G, to obtain slump between 125mm to 175 mm. Coarse Aggregate Crushed natural rock with a 10-mm maximum size. Fine Aggregate Washed, natural river sand with a fineness module of 3.0. Age Number of Days Compressive strength Experimental results of destructive testing on 15-cm cylinders

Good luck