# MATH301-Data Driven Statistics- Hypothesis Testing – Part III Regression and Correlation

Part III: Regression and Correlation Based

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For Susan Athena:

Part III: Regression and Correlation

Based on what you have learned from your research on regression analysis and correlation, answer the following questions about the Body Fat Versus Weight data set:

•When performing a regression analysis, it is important to first identify your independent/predictor variable versus your dependent/response variable, or simply put, your x versus y variables. How do you decide which variable is your predictor variable and which is your response variable?

•Based on the Body Fat Versus Weight data set, which variable is the predictor variable? Which variable is the response variable? Explain.

•Using Excel, construct a scatter plot of your data.

•Using the graph and intuition, determine whether there is a positive correlation, a negative correlation, or no correlation. How did you come to this conclusion?

•Calculate the correlation coefficient, r, and verify your conclusion with your scatter plot. What does the correlation coefficient determine?

•Add a regression line to your scatter plot, and obtain the regression equation.

◦Does the line appear to be a good fit for the data? Why or why not?

◦Regression equations help you make predictions. Using your regression equation, discuss what the slope means, and determine the predicted value of body fat (y) when weight (x) equals 0. Interpret the meaning of this equation.

Your analysis is now complete, in one paragraph, summarize your results by explaining your findings from the statistical measures, hypothesis test, and regression analysis of body fat and weight for the 252 men attending Silver’s Gym.

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