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Simple Linear Regression and Correlation

Simple Linear Regression and Correlation. Prepared by: Paolo lorenzo Bautista. Simple Linear Regression. In SLR, we assume one dependent and one independent variable. We try to predict the outcome/result of a dependent variable based on the independent variable

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Simple Linear Regression and Correlation

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  1. Simple Linear Regression and Correlation Prepared by: Paolo lorenzo Bautista

  2. Simple Linear Regression In SLR, we assume one dependent and one independent variable. We try to predict the outcome/result of a dependent variable based on the independent variable Example: The intelligence test scores of 12 college freshmen were obtained, and we try to find out if this has an effect on the freshmen’s chemistry grade. SLR : PLBautista

  3. Simple Linear Regression SLR : PLBautista

  4. Simple Linear Regression • We wish to find a line of the form y = a + bx which will tell us the trend shown by the data. • Using PHStat, we have y = 30.0433 +0.8972x • Predict a freshman’s chemistry grade if his intelligence test score is 70. • What should a freshman’s intelligence test score be if he wants a grade of 90 for chemistry? • Provide an interpretation of the slope. SLR : PLBautista

  5. Correlation Analysis Measures the strength of relationships between two variables by means of a number called the correlation coefficient. Also called the Pearson correlation coefficient. SLR : PLBautista

  6. Correlation Analysis Photo from wikipedia SLR : PLBautista

  7. Correlation Analysis Example: Find the correlation coefficient from our previous example. r = 0.8625 indicating a strong positive linear relationship Coefficient of Determination (r2) – the percentage of the variation in the dependent variable (Y) that can be explained by a linear relationship with the independent variable (X) r2 = 0.7438 meaning 74.38% of the variation in chemistry grades is explained by a linear relationship with intelligence scores SLR : PLBautista

  8. Correlation Analysis May require careful personal inspection SLR : PLBautista

  9. Hypothesis Testing for Correlation H0: ρ=0 H1: ρ≠0 (significant linear association between X and Y) t-test with n-2 degrees of freedom Test statistic: SLR : PLBautista

  10. Exercise The following data show the amount of money 8 companies used for advertising, and the corresponding sales: SLR : PLBautista

  11. Exercise Provide the estimated regression equation to predict sales given the amount spent on advertising. Provide an interpretation of the slope. What is the expected sales of a company if it spends $45 for advertising. Compute the correlation coefficient. Interpret. Compute the coefficient of determination. Interpret. Test if there is a significant linear association between advertising and sales. SLR : PLBautista

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