Correlation Coefficient, r. Pearson Product Moment Correlation Coefficient, r
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1 Best fit line GOALS: 1. Associate a regression equation with the correlation coefficient, r. 2. The correlation coefficient, r, provides a measure of how well a straight line fits the data, or how strong a linear relationship exists between the two variables. 3. Compute r from the coefficient of correlation: r = r 2 4. The value of r can range from: 1 < r < 1 5. When r < 0, there is a negative correlation between the variables. 6. When r > 0, there is a positive correlation between the variables. Study Ch. 14.4, # , 145, 147 [# , 122, 123, 125] Class Notes Homework Pearson Product Moment Measure of the strength of the linear relationship between two variables. linear not linear G. Battaly
2 Pearson Product Moment 1 r 1 r > 0 regression line has positive slope variables are positively linearly correlated r < 0 regression line has negative slope variables are negatively linearly correlated r near +1 or 1 indicates strong linear relationship r near 0 indicates weak linear relationship G. Battaly
3 Find on Calculator: STAT / TESTS / LinRegTTest xlist: L1 Ylist: L2 2 tailed, left tailed, right tailed calculate Output: y=ax+b 2 tailed, rt tailed, lf tailed t= p= df= a = b = s = r 2 =. r = 14.3 Coefficient of Determination geogebra A random sample of custom homes for sale include the following information: a size of x hundred sq. ft selling at $ y thousand. Predict the price of a home that is 3100 ft. Is the correlation between size and price weak or strong? x y G. Battaly
4 # 124 Predict the cost of a home with 3100 sq ft. geogebra solution Gertrude Battaly, Coefficient of Determination geogebra A random sample of custom homes for sale include the following information: a size of x hundred sq. ft selling at $ y thousand. Predict the price of a home that is 3100 ft. Is the correlation between size and price weak or strong? x y r = 0.8 r is closer to 1 than to 0. This suggests a strong positive linear relationship between size and price The t test for the population correlation coefficient H o : ρ = 0, H a : ρ 0 indicates the p value: p=.0058 This shows very strong evidence that a linear relationship exists and that the regression line is a good predictor. Use LinRegTTest to get r G. Battaly
5 14.3 Coefficient of Determination Hours of Study vs. Test Scores: How are the hours of study and test scores related? r = hrs test x y r is closer to 1 than to This suggests a negative linear relationship between hours of study and test grades The t test for the population correlation coefficient H o : ρ = 0, H a : ρ 0 indicates the p value: p=.024 This shows strong evidence that a linear relationship exists and that the regression line is a good predictor. Class Notes Homework Use LinRegTTest to get r G. Battaly
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