Question

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?

Answer 1

To estimate the average January temperature for Pittsburgh using the regression equation y = 49.4 - 0.313x, substitute the latitude of Pittsburgh (40) into the equation. The estimated average January temperature for Pittsburgh is 36.88 degrees Fahrenheit.

Step-by-step explanation:

The student has asked about estimating the average January temperature for Pittsburgh based on a given regression equation. The regression equation provided is y = 49.4 - 0.313x, where y represents the average January temperature in degrees Fahrenheit, and x represents the latitude in degrees. To estimate the temperature for Pittsburgh, which is located at latitude 40, we substitute x with 40 in the equation.

Using the regression equation, the calculation is as follows:

y = 49.4 - 0.313(40), which simplifies to:

y = 49.4 - 12.52

y = 36.88 degrees Fahrenheit.

Therefore, the estimated average January temperature for Pittsburgh is 36.88 degrees Fahrenheit based on the regression equation.

Answer 2

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.