Question

Using the daily high and low temperature readings at Chicago's O'Hare International Airport for an entire year, a meteorologist made a scatterplot rel

Scatterplots
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asked 2021-07-04

Using the daily high and low temperature readings at Chicago's O'Hare International Airport for an entire year, a meteorologist made a scatterplot relating y = high temperature to x = low temperature, both in degrees Fahrenheit.

After verifying that the conditions for the regression model were met, the meteorologist calculated the equation of the population regression line to be  \(\left[\mu_y=16.6+1.02\right] with \left[\sigma = 6.6+^\circ F\right]\)

If the meteorologist used a random sample of 10 days to calculate the regression line instead of using all the days in the year, would the slope of the sample regression line be exactly 1.02? Explain your answer.

Answers (1)

2021-07-05
No, because the slope of the population regression line is 1.02 and we expect the slope of the sample regression line to be close 1.02 (but not exactly 1.02) as there is some sampling variability in a sample.
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