The data given in the following table shows equivalent temperatures on the Celsius temperature scale and the Fahrenheit temperature scale

Question

The data given in the following table shows equivalent temperatures on the Celsius temperature scale and the Fahrenheit temperature scale. (A graphing calculator is recommended. Round your answers to two decimal places.)

Celsius (x°)	−40     0    100
Fahrenheit (y°)	−40    32    212

(a) Find the linear correlation coefficient for the data.

(b) What is the significance of the value found in part (a)?

-The value in part (a) is insignificant.

-The correlation obtained by the data is not linear.    

-The value in part (a) is a perpendicular line.

-The data displays a perfect linear relationship.

-The data displays a quadratic relationship.

(c) Find the equation of the least-squares regression line.

ŷ = 

 

(d) Use the equation of the least-squares line from part (c) to predict the Fahrenheit temperature that corresponds to a Celsius temperature of 20°.

=____ °F

(e) Is the procedure in part (d) an example of interpolation or extrapolation?

-interpolation

-extrapolation    

Answer 1

212 = 9/5 x 100 + 32 = 180+32 = 212

32 = 9/5 x 0 + 32 = 32

F = (9/5)C + 32

or

C = (5/9)(F-32)

r or correlation = 1. R^2 = 1, It's a perfect linear relationship, by definition

if experimental data showed something else, it would be unreliable data or mistake in recording it.

if C =-40, F= (9/5)(-40) + 32 = -72+32 = -40

if C= 20 F=(9/5)(20) +32 = 36 +32 = 68

20 is between 0 and 100, 68 is between 32 and 212, so it's interpolation extrapolation is going outside the range of values.