Question

Use the least squares regression line of this data set to predict a value.
The design team at an electronics company is evaluating its new prototype for a miniature recording device. As part of this evaluation, designers at the company gathered data about competing devices already on the market.
Among other things, the designers recorded the thickness of each recording device (in millimeters), x, and its maximum recording length (in minutes), y.
Thickness (in millimeters) Recording time (in minutes)
11.26 152
11.60 221
22.75 254
24.41 354
24.85 464
28.31 319
The least squares regression line of this data set is:
y=11.482x+58.266
How much recording time does this line predict for a device 22.58 millimeters thick?
Round your answer to the nearest integer.
minutes

Answer 1

To predict the recording time for a device that is 22.58 millimeters thick using the least squares regression line equation \( y = 11.482x + 58.266 \), we can substitute \( x = 22.58 \) into the equation.

\[
y = 11.482(22.58) + 58.266
\]

First, calculate \( 11.482 \times 22.58 \):

\[
11.482 \times 22.58 = 259.37476
\]

Next, add 58.266 to that result:

\[
y = 259.37476 + 58.266 = 317.64076
\]

Now, rounding this to the nearest integer, we get:

\[
y \approx 318
\]

Thus, the predicted recording time for a device that is 22.58 millimeters thick is **318 minutes**.