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 [\mu_y=16.6+1.02] with [\sigma = 6.6+^\circ F]. About what percent of days with a low temperature of 40^\circ F?

Question
Scatterplots
asked 2020-10-20
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 \(\displaystyle{\left[\mu_{{y}}={16.6}+{1.02}\right]}{w}{i}{t}{h}{\left[\sigma={6.6}+^{\circ}{F}\right]}\).
About what percent of days with a low temperature of \(\displaystyle{40}^{\circ}\) F?

Answers (1)

2020-10-21
Step 1
Given:
\(\displaystyle{\left[\mu_{{y}}={16.6}+{1.02}{x}\right]}\) (Equation population regression line)
\(\displaystyle{\left[\sigma={6.64}\right]}\)
The average high temperature on days where the low temperature is \(\displaystyle{40}^{\circ}\) F according to the population regression line can be found by replacing 2 in the regression line equation by 40 and evaluating.
\(\displaystyle{\left[\mu_{{y}}={16.6}+{1.02}{\left({40}\right)}={16.6}+{40.8}={57.4}\right]}\)
Result:
\(\displaystyle{57.4}^{\circ}{F}\).
0

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