Question

For each of the problems below: A. Draw a scatterplot. B. Calculate Pearson's r C. Calculate the y-intercept, slope, and draw a regression line on the scatterplot. D. Answer the “Prediction" problem. E. Calculate r and explain what it tells us about the relationship between the variables. F. Calculate the t-ratio for Pearson's r and deter- mine the level of significance. 1. Sociologists have discovered a phenomenon known as "environmental racism," a condition that exists when people of color bear a disproportionate burden of en- vironmental hazards relative to whites. Suppose we sample 10 communities to determine the number of toxic waste sites in each community and the percent of each community's population that is nonwhite. Use the data in the table below to answer the six questions above. I PERCENT PEOPLE OF COLOR (X) NUMBER OF TOXIC WASTE SITES (Y بيا 6 20 14 14 10 3 4 9 8 22 17

Answer 1

y 20 18 y = 0.5417x + 1.4167.0 14 8 6 4 O 0 5 10 15 20 25 30 35

The pearson's to = nEXY ExY) nex" - (2x)" ΣΥ' (Σ) 1081611 140 x 90 10x2608 19600 dioxio 44 - 8100 O. 9014. Let the regression line is. Y; - Bot B, 2; t&: begression line is , = $c + B, ; y- intercept Å, {%;X; - EY; EX, the estimated the n {x; - (2x;)" n 1611 I Gox.go 10 2608 1400 -10 0.5417 the slope parameter 3 ý É 9-0.5417814 1.4 162 1416 the negression line is (estinated) Y = 1.416 + 0.5417 x; you from the can predict any percent people of color regression ca. } = 1.416 +0.5417 ni

6.8125 for y can be E the value ob b = (6. go4) = 0.8125. b indicates the variability of proportion is which caused by it's relationship with the variable x, proportion is very kind high, it indicates very strong tit of the relationship Th's the t-ratio for the pearson's his til t- - b N-2 0.90148 13.597 tbt 1- 0.8125 you choose the level of significance.