Session 1. Introduction to R and R Commander (Rcmdr) and R functions for basic statistical models

(a) Preliminaries

Instructions for downloading and installing R. [Link for downloading R.]

R Commander (Rcmdr) is installed from within R.

Current version for R is 3.2.1, and for Rcmdr 2.1-7.

We will be using Wolfgang Jank's book Business Analytics for Managers (Use R!) in Session 2 which  can be purchased from amazon.com.

(b) R functions

The "theory" (i.e., background material) behind the techniques described below will be given after each example.

b.1 Graphics in R

Example: Let's use the Direct marketing data set (as a .csv file) to plot some amazing graphs via Rcmdr. Graphics obtained from Rcmdr in this dataset are here as a .pdf file.

b.2 Probability calculations

Binomial distribution

Example: Historical records indicate that 40% of all customers who enter a discount store make a purchase. What is the probability that two of the next three customers will make a purchase?

This is a binomial problem. The result is 0.288 as shown in this file. This is obtained in Rcmdr via the steps, Distributions > Discrete Distributions > Binomial Distribution > ... Try to replicate the results.

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Normal distribution

Example: Distribution of fuel efficiencies of a new model car, X, is normal. Assuming that X ~ N(7.13,0.27^2) find the probability Pr(6.75 < X < 7.49).  Here is the result from Rcmdr.

b.3 Confidence intervals

Example: (Population mean) A company's financial health is (usually) measured using its debt-to-equity ratio. A bank has collected n = 15 of its commercial accounts in this file. Let's find the 95% confidence interval (CI) using Rcmdr. (This is done via the t-test command which includes the CI. Here is the result.

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Example: (Population proportion) The CI for population proportion is easy to obtain. Suppose you poll 1000 people and 340 of them state that they would vote Liberal, if the election were held today. Here is what we do to find a 95% CI:

> prop.test(340,1000)

1-sample proportions test with continuity correction

data: 340 out of 1000, null probability 0.5
X-squared = 101.761, df = 1, p-value < 2.2e-16
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
0.3108142 0.3704312
sample estimates:
p
0.34

So, the sample proportion is 0.34, with a 95% CI of [0.3108,0.3704], i.e., a margin of error of about 3%.

b.4 Hypothesis testing

Hypothesis testing in R (with one or two populations) still uses the t.test function described above. We now discuss a problem with two populations.

Example: The data set concerns the weight losses experienced by dieters using the Atkins diet or the conventional diet. We want to test the hypothesis that there is no difference between the two methods. Here are the results from Rcmdr.

b.5 ANOVA

The final example involves analysis of variance (ANOVA) where we want to test the null hypothesis that three or more population means are equal. Once again, Rcmdr solves this problem quite admirably.

Example: (One-way ANOVA) Let's consider a problem from agricultural testing in an experimental farm. We want to test the null hypothesis that low (L), medium (M) or high (H) fertilizer levels do not differ in their effects on the average yield of a new plant. We have 18 small plots, and on six randomly selected plots we use L, the other six M and the last six H. Here is the data set for this example. Rcmdr uses the R function aov and finds these results.

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Example: (Two-way ANOVA) Note that the above example is a one-factor ANOVA problem. R can of course deal with multi-factor problems, too. Consider the data in this file where we have two factors: Shelf display height (Bottom, Middle, Top) and shelf display width (Regular, Wide). The numbers in each cell correspond to sample group means (sales) for the last six months from three different stores. This is a 2 x 3 (or, 3 x 2) design.

We want to test three hypotheses: (i) There is no interaction between the factors, (ii) Factor 1 (height) has no effect on sales, (iii) Factor 2 (width) has no effect on sales. These results show that (i) little or no interaction exists between height and width (high p-value), (ii) height affects the sales (p-value near zero), (iii) width does not affect sales (high p-value). Here, the p-values are denoted by Pr(F>).