A regression was done for 20 cities with latitude as the explanatory variable (x) and average january temperature as the response variable (y). the latitude is measured in degrees and average january temperature in degrees fahrenheit. the latitudes ranged from 26 (miami) to 47 (duluth). the regression equation is y = 49.4 - 0.313 x. the city of pittsburgh, pennsylvania has latitude 40 degrees with average january temperature of 25 degrees fahrenheit. what is the estimated average january temperature for pittsburgh, based on the regression equation?

Question

Lucas Callahan

Mathematics

24 September, 10:42

A regression was done for 20 cities with latitude as the explanatory variable (x) and average january temperature as the response variable (y). the latitude is measured in degrees and average january temperature in degrees fahrenheit. the latitudes ranged from 26 (miami) to 47 (duluth). the regression equation is y = 49.4 - 0.313 x. the city of pittsburgh, pennsylvania has latitude 40 degrees with average january temperature of 25 degrees fahrenheit. what is the estimated average january temperature for pittsburgh, based on the regression equation?

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Miriam Hines · Answer 1

Based on the regression equation, y = 49.4 - 0.313 x, where x is lattitude and y is average estimated january temperature, the expected temp fo Pittsburg, at a lattitude of 40, is 49.4 - (0.313 * 40), or 36.88 degrees fahrenheit. This differs, by 11.88 deg f from the measured report of 25 deg f for January tepuratues in Pittsburg.