The exponential regression equation is y = 172.21(0.99)ˣ and at x = 60 minutes y = 94.22 degree Fahrenheit and at x = 240 minutes y = 15.43 degree Fahrenheit.
What is correlation?
It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]
We have data shown in the table:
We can find the exponential regression equation using the data shown.
[tex]\rm y = ab^x[/tex]
After calculating from the data:
a = 172.21 and b = 0.99
[tex]\rm y = 172.21(0.99)^x[/tex]
The correlation coefficient will be:
r = -0.99
The range will be all real numbers.
The domain will be y > 0
As we can see in the graph x ∈R and y>0
After an hour,
Plug x = 60 minutes in the exponential regression equation:
[tex]\rm y = 172.21(0.99)^{60}[/tex]
y = 94.22 degree Fahrenheit
After 4 hours, plug x = 240
[tex]\rm y = 172.21(0.99)^{240}[/tex]
y = 15.43 degree Fahrenheit
Similarly, we can find any data from the exponential regression equation.
Thus, the exponential regression equation is y = 172.21(0.99)ˣ and at x = 60 minutes y = 94.22 degree Fahrenheit and at x = 240 minutes y = 15.43 degree Fahrenheit.
Learn more about the correlation here:
brainly.com/question/11705632
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