Answer:
a)
y = 0.3035 + 0.0082x
b)
0.6315 mm
c)
x = 23.9634 °C
Step-by-step explanation:
a. Compute the least-squares line for predicting warping from temperature. Round the answers to four decimal places.
We need to find an equation of the form
y = b + mx
where m is the slope and b the Y-intercept.
The slope m can be computed with the formula
[tex]\bf m=\displaystyle\frac{\displaystyle\sum_{i=1}^n(x_i-\bar x)(y_i-\bar y)}{\displaystyle\sum_{i=1}^n(x_i-\bar x)^2}[/tex]
Replacing the values in our formula (we will round at the end of the calculations)
[tex]\bf m=\displaystyle\frac{806.94}{98,775}=0.008169476[/tex]
the Y-intercept b is computed with the formula
[tex]\bf b=\bar y-m\bar x[/tex]
therefore we have
[tex]\bf b=0.5188-0.008169476*26.36=0.303452613[/tex]
and the least-squares line rounded to 4 decimals would be
y = 0.3035 + 0.0082x
b. Predict the warping at a temperature of 40°C. Round the answer to three decimal places.
We simply replace x with 40 to get
y = 0.3035 + 0.0082*40 = 0.6315 mm
c. At what temperature will we predict the warping to be 0.5 mm? Round the answer to two decimal places
Here, we replace y with 0.5 and solve for x
0.5 = 0.3035 + 0.0082x ===> x = (0.5-0.3035)/0.0082 ===>
x = 23.9634 °C
