## Introduction to Probability Models

Lecture 41

Qi Wang, Department of Statistics

Dec 6, 2017

## Graphs: Qualitative Data

### Example 1

• Frequency distribution is the frequency or count of the occurrences within a particular category
• Relative frequency distribution is the proportion/percentage of the occurrences within a particular category
Place of Purchase # of Students % of Students
University/Follett’s Bookstore 106 53%
Amazon.com or Half.com 50 25%
Previous students 22 11%
Purchase e-book 22 11%

### Bar Graph

Typically with bar graphs, the y-axis represents the frequency (# of observations) in the categories. Elements can give multiple answers or no answer.Pay attention to the axes.

### Pie Chart

Pie Chart is circular graph in which the relative size of the “slice” represents the percents or proportion of responses in that category. Percents must add to 100%. Each element/subject is allowed to give only one answer.

## Graphs: Quantitative Data

### Dot Plot

Dot Plot is a graphical device that summarizes data by the number of dots above each data value on the horizontal axis.

### Line Graph

Line Graph is a graphical device that summarizes time series data.Time/date is usually on the horizontal axis and the value of the measured variable on the vertical axis. Look for upward or downward trends. Look for seasonal patterns

## Comparing Some of the Graphs

### Example 2

What type of graph would be appropriate in order to answer the following questions?

• What percentage of a household budget was spent on housing, utilities, food, insurance, entertainment, transportation and other?
• What values represent the middle 50% of the data for miles per gallon (mpg) of a sample of 2008 Toyota Camrys?
• How did the daily closing price of one share of Intel Corporation (INTC) stock fluctuate in the First quarter of 2012?
• Are gas prices and daily high temperature related
• A poll of 300 Purdue University students was taken. How many students in the poll purchased food from each of the following restaurants in the past month: Jimmy Johns, Chipotle, Noodles, Buffalo Wild Wings and Panera?

## More on Regression

### Example 3

Drew wanted to prove to his friend Steve that World of Warcraft (WOW) was bad for his education. He collected data from friends in Stat 225 that play WOW. The plot below reflects his findings.

1. What is the explanatory variable and what is the response variable?
2. What is the slope of this line? What does this value mean in terms of the story?
3. How much of the variation in the STAT 225 exam score is NOT explained by the linear relationship with the number of hours spent playing WOW per week?
4. What is the value of the correlation between exam score and the number of hours per week spent playing the game?
5. Suppose a student played WOW for 23 hours per week. What is his/her predicted STAT 225 Exam Score? Is this predicted value valid? Why or why not?
6. If the number of hours playing WOW were to decrease by 2.5 hours per week, by how much would you expect the STAT 225 Exam Score to change?

### Example 4

The following scatterplot was created from 2 quantitative variables, x and y. Choose the correct statement that relates to this figure.

• A. The correlation would be close to 0.
• B. $r^2 < 0$
• C. For each 1 unit increase in x, there is an expected increase in y
• D. For each 1 unit increase in x, there is an expected decrease in y.
• E. Cannot make any definitive statements without additional information