Dataset temperature is available here. The average January temperatures ( y ) and geographic latitudes ( x ) of 20 cities in the United States are given in the dataset. The regression equation for...

Dataset temperature is available here.

The average January temperatures (y) and geographic latitudes (x) of 20 cities in the United States are given in the dataset. The regression equation for these data is

ŷ = 126 − 2.34x.

Use the regression equation given above to answer the following question.

(a)

What is the slope of the line?

Interpret the slope in terms of how mean January temperature is related to change in latitude.

The slope gives the average January temperature at the equator.The slope gives the average latitude of cities with an average January temperature is 0 degrees. The slope gives the average change in average January temperature for each one unit increase in latitude.The slope gives the average change in latitude for each one degree increase in the average January temperature.

(b)

Pittsburgh, Pennsylvania, has a latitude of 40, and Boston, Massachusetts, has a latitude of 42. Use the slope to predict the difference in expected average January temperatures for these two cities. Compare your answer to the actual difference in average January temperatures for these two cities using the data. (Use Boston − Pittsburgh.)

The predicted difference in average January temperatures was . This indicates that the predicted average January temperature in Pittsburgh is than the predicted average January temperature in Boston. The actual average Janurary temperature in Pittsburgh is the average January temperature in Boston. Thus, the results .

(c)

Predict the average January temperature for a city with latitude 41.

(d)

Refer to part (c). Identify the two cities in the table that have a latitude of 41 and compute the residual (prediction error) for each of these cities. Discuss the meaning of these two residuals in the context of this example, identifying whether each city is warmer or cooler than predicted.

The first city, , has a residual of which indicates the city is than predicted. The second city, , has a residual of which indicates the city is than predicted.

Jun 09, 2022

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Dataset temperature is available here. The average January temperatures ( y ) and geographic latitudes ( x ) of 20 cities in the United States are given in the dataset. The regression equation for...

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