1 Water Usage of Production Plant

A production plant cost-control engineer is responsible for cost reduction. One of the costly items in his plant is the amount of water used by the production facilities each month. He decided to investigate water usage by collecting seventeen observations on his plant’s water usage and other variables.

fn.data <- "http://statacumen.com/teach/ADA2/homework/ADA2_HW_02_water.txt"
water <- read.table(fn.data, header=TRUE)
str(water)
'data.frame':   17 obs. of  5 variables:
 $ Temperature: num  58.8 65.2 70.9 77.4 79.3 81 71.9 63.9 54.5 39.5 ...
 $ Production : int  7107 6373 6796 9208 14792 14564 11964 13526 12656 14119 ...
 $ Days       : int  21 22 22 20 25 23 20 23 20 20 ...
 $ Persons    : int  129 141 153 166 193 189 175 186 190 187 ...
 $ Water      : int  3067 2828 2891 2994 3082 3898 3502 3060 3211 3286 ...
#summary(water)

Note: Because of the high correlation between Production and Persons, do not include Persons in the model.

2 Rubric

Following the in-class assignment this week, perform a complete multiple regression analysis.

  1. (1 p) Scatterplot matrix and interpretation
  2. (2 p) Fit model, assess multiple regression assumptions
  3. (1 p) Interpret added variable plots
  4. (1 p) If there are model assumption issues, say how you address them at the beginning and start again.
  5. (1 p) State and interpret the multiple regression hypothesis tests
  6. (2 p) Interpret the significant multiple regression coefficients
  7. (1 p) Interpret the multiple regression \(R^2\)
  8. (1 p) One- or two-sentence summary

3 Solutions

3.1 (1 p) Scatterplot matrix

A parallel coordinate plot is another way of seeing patterns of observations over a range of variables.