Unit 5: Regression & Correlation Week 1

Data Relationships Finding a relationship between variables is what we’re looking for when extracting data from sample populations. Is education better or worst now than before? Do students learn better with the use of technology in the classroom? Does proper sex ed. help prevent STDs and teen pregnancy?

Data Relationship Studies to find correlation and regression start with a graph. Scatterplot: a graph with order pairs (X,Y) plotted in a x-y coordinate plane. Response Variable (Y): Measures the outcome of the study. Usually known as the dependent variable Explanatory Variable (X): explains or affects, changes the outcome (response variable). Also known as the independent variable.

Scatterplots. Shows the relationship between two quantitative variables measured on the same individual or study. What to look for in a scatterplot? Look for a linear pattern Describe scatterplots by using: Form: Linear correlation, non linear or no correlation. Direction: Positive or negative correlation. Strength: Strong, moderate, or weak correlation.

Google Classroom Code 6 th Period: j6vaan

Exercise #1 Identify the explanatory and the response variables 1. An experiment was conducted to test the effects of sleep deprivation on human response time. 2. Measuring the effects of detergent concentrations on germination of seeds. 3. Analyzing the test scores and the hours of sleep. 4. The number of weeks a CD has been out and the total sales

Example Classify your response and explanatory variables, draw the scatterplot of your data set and describe it. 1. In one of the Boston city parks a cadet took a random sample of 10 days and compiled the following data. For each day, x represents the number of police officers on duty in the park and y represents the number of reported muggings on that day Police officers Reported Muggings

Exercise #2 Classify your response and explanatory variables, draw the scatterplot of your data set and describe it. We want to determine if there is an association between the temperature (weather) and ice cream sales. We want to determine if there is a relationship between the number of weeks a CD has been out and the number of sales Temp °C Ice cream Sales $ $215$325$185$332$406$522$412 Weeks Sales $

Correlation Correlation: a mutual relationship or connection between two things. Test grades and hours of study CD sales and weeks on the market Ice cream sales and crime rate ** The fact that there is a correlation does not mean that it is the cause of the other.

Correlation =/= Causation

Linear and Non Linear Correlation

Properties of the correlation coefficient r tells you the strength and direction of the correlation r has no units. - 1 ≤ r ≤ 1 If r > 0 there is a positive correlation If r < 0 there is a negative correlation If r = 0 there is NO correlation

Correlation Coefficient The closer r is to 1 or -1 the stronger it is.

Describe the strength and direction of the following correlations

How to find the correlation coefficient

Finding the Correlation coefficient Example: We want to determine if there is an association between the height and the scoring average of the women in a basketball team. Height Scoring Average

Is the correlation coefficient significant? Remember: we use small samples to make predictions about a population. Based on a few pairs of data points, can we make an inference about the population of all such data points? If we decide that the correlation is significant to make a prediction about a population, then we use a level of significance Significant levelα = 0.05 indicates a 5% risk of concluding that there exist a difference when there is no actual difference.

Example for significance We used 6 pairs of data to find r=0.94. Is the correlation coefficient significant using α = 0.05? Take the absolute value of r Since 0.94 > 0.811, we can conclude that the population correlation is significant. Conclusion: There is enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between the height of basketball players and their scoring average. Height Scoring Average

Example: Hours of exercise, X GPA, Y a)Find r: b)Interpret r: c)Is the correlation coefficient significant using α = 0.05? d)Conclusion:

Least Square Regression Line