PS 3: Sections 110 & 111

Transcription

1 PS 3: Sections 110 & 111 GSI: L. Jason Anastasopoulos University of California, Berkeley April 3, 2013

2 For today 1. Standard Deviation 2. Correlation 3. Regression

3 Standard Deviation S = N i=1 (X i X) 2 N 1 Standard deviation is a measure of spread which captures how widely dispersed a set of data is. Generally very useful for understanding how tightly (or loosely) observations cluster around the mean.

4 Standard Deviation Question: Which variable has the higher standard deviation?

5 Standard Deviation Question: Using the information below, rank the variables (high to low) by standard deviation. Mean Min Max Robberies/Capita Burglaries/Capita Rape/Capita Crime Rates for all 50 States:

6 Standard Deviation Question: Using the information below, rank the variables by standard deviation. Mean Min Max SD Rank Robberies/Capita Burglaries/Capita Rape/Capita Crime Rates for all 50 States:

7 Correlation A relationship between two or more variables (X and Y). Types of correlation: Positive - as X increases, Y increases and vice versa. Ex) Shoe size and height, number of cars on the road number of car accidents. Negative - as X increases, Y decreases and vice versa. Ex) Alcohol consumption and number of good decisions made, vacation days and productivity. Zero - no relationship between X and Y. Ex) Number of cars parked at the Rockridge Bart and number of stars in the universe. Ways of assessing correlation: Numerically - correlation coefficient - r. Visually - scatter plots of two variables.

8 Assessing Correlation: r The correlation coefficient r basically measures how strongly two variables are related. Properties of r: 1 r 1 r > 0 = positive correlation. r < 0 = negative correlation. r = 1 = a perfect negative correlation. r = 1 = a perfect positive correlation.

9 Assessing Correlation: r and scatterplots Scatterplots can visually demonstrate correlation. Figure: State White Unemployment v. Black Unemployment, : Positive Correlation

10 Assessing Correlation: r and scatterplots Scatterplots can visually demonstrate correlation. Figure: Democratic House Vote Share v. Republican House Vote Share, : Positive Correlation

11 Assessing Correlation: Questions Question Given the scatterplot below: (1) Is r positive or negative?; (2) Is r closer to: (a) 1, (b) 0.5, (c) 0, (d) -0.5, (e) -1 Figure: Temperature v. Precipitation, 50 States,

12 Assessing Correlation: Questions Question Given the scatterplot below: (1) Is r positive or negative?; (2) Is r closer to: (a) 1, (b) 0.5, (c) 0, (d) -0.5, (e) -1 Figure: Male Unemployment v. Female Unemployment, 50 States,

13 Assessing Correlation: Questions Question Given the scatterplot below: (1) Is r positive or negative?; (2) Is r closer to: (a) 1, (b) 0.5, (c) 0, (d) -0.5, (e) -1 Figure: Democratic v. Republican House Vote Share, 50 States,

14 Introduction to Regression Regression is a tool used to make predictions and describe relationships between two or more variables. Bivariate regression involves two variables, multivariate regression involves three or more variables. A straight line fit to a scatterplot is used to predict how a one-unit increase in one variable changes with a one unit increase in another. Example: Is Weather Related to Crime?

15 Introduction to Regression Example: Is Temperature Related to Crime? ˆ Murder = Temperature r = 0.70 Figure: Temperature v. Murders Per Capita, 50 States,