Answer:
69 °F
Step-by-step explanation:
The regression line of [tex]y[/tex] on [tex]x[/tex] is: [tex]y = a + bx[/tex]
(where [tex]a[/tex] is the y-intercept and [tex]b[/tex] is the slope)
From inspection of the graph:
[tex]\textsf{slope}\:(b)=\dfrac{\textsf{change\:in}\:y}{\textsf{change\:in}\:x}=\dfrac13[/tex]
Using point (66, 58) and the found value of b to find the equation of the regression line:
[tex]\implies y-58=\dfrac13(x-66)[/tex]
[tex]\implies y=36+\dfrac13x[/tex]
To find the likely outside temperature if the crickets were measured to chirp 99 times in one minute, simply substitute [tex]x=99[/tex] into the equation:
[tex]\implies 36+\dfrac13(99)=69[/tex]
Important:
When we use values of x outside the range of the original data to predict corresponding values of y, it is call "extrapolation". These predictions can be unreliable because there is no evidence that the relationship described by the regression line is true for all values of x.
