In: Statistics and Probability
A researcher is interested in examining the relationship between social isolation for older adults (x), defined as the percentage of the people over the age of 65 who live alone, and eldercide rates (y), defined as the homicide rate for people over age 65 per 100,000. Collecting data from 195 cities, they find the following: top enclose x equals 30.95 s subscript x equals 5.96 top enclose y equals 2.80 s subscript y equals 5.71 r subscript x y end subscript equals.35 With this information in mind, please do the following: First, calculate the slope of the regression line using the formula covered in class: Next, calculate the y-intercept of the regression line using the formula covered in class: Using the results from the slope and y-intercept calculations above, interpret the regression results as fully as possible making sure to discuss it in the context of the problem. Be sure to write out the regression equation as part of this interpretation. Using the results from above, calculate the predicted eldercide rate for a city where 28% of older Americans live alone. Finally, identify what proportion of the variation in eldercide rates is explained by the percentage of older Americans living alone.