An article gave data on a measure of pollution (in micrograms of particulate mat

Question

An article gave data on a measure of pollution (in micrograms of particulate matter per cubic meter of air) and the cost of medical care per person over age 65 for six geographical regions of the United States. Find the equation of the least-squares line describing the relationship between y = medical cost and x = pollution. (Give the answer to two decimal places.) y hat = Region Pollution Cost of Medical North 29.5 929 Upper South 31.3 905 Deep South 31.6 982 West South 26.3 986 Big Sky 29.9 966 West 39.5 913

Explanation / Answer

The regression equation is given by y - mean y = Sxy/(Sx)2 * (x - mean x)

Where Sxy = [Sum(xy)/n] - mean x * Mean y

and (Sx)2 = Sum(x2)/n - (Mean x)2

The table below gives the required values for the above calculations:

Mean x = 188.1/6 = 31.35, Mean y = 5681/6 = 946.83, Sum(xy) = 177641.9, sum(x2) = 5994.95

mean x * mean y = 31.35 * 946.83 = 29683.12 and (mean x)2 = 982.82

Sxy = 177641.9/6 - 29683.12 = -76.14

(Sx)2 = 5994.95/6 - 982.82 = 16.34

and Sxy/(Sx)2 = -76.14/16.34 = -4.66

Therefore y - 946.83 = -4.66(x - 31.35)

Solving y = 946.83 - 4.66x + 146.091

or y = -4.66x + 1092.92

Count x y xy x2 y2 1 29.5 929 27405.5 870.25 863041 2 31.3 905 28326.5 979.69 819025 3 31.6 982 31031.2 998.56 964324 4 26.3 986 25931.8 691.69 972196 5 29.9 966 28883.4 894.01 933156 6 39.5 913 36063.5 1560.25 833569 Total 188.1 5681 177641.9 5994.45 5385311

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