Question

Use the least squares regression line of this data set to predict a value.
To plan its upcoming programming, a local television station wanted to study the television watching habits of people in the area. Station executives called a random sample of people in their broadcast area and asked them a variety of questions.
In particular, they asked people their ages, x, and how many hours of television they had watched last week, y.
Age Hours
17 0
26 7
68 19
68 15
76 20
The least squares regression line of this data set is:
y=0.303x–3.233
How many hours of television does this line predict a 46-year-old would have watched last week?
Round your answer to the nearest thousandth.
hours

Answer 1

To predict the number of hours of television a 46-year-old would have watched using the least squares regression line \( y = 0.303x - 3.233 \), we simply need to substitute \( x = 46 \) into the equation.

\[
y = 0.303(46) - 3.233
\]

Calculating \( 0.303 \times 46 \):

\[
0.303 \times 46 = 13.938
\]

Now, substituting this value back into the equation:

\[
y = 13.938 - 3.233
\]

Calculating \( 13.938 - 3.233 \):

\[
y = 10.705
\]

Thus, the predicted number of hours of television a 46-year-old would have watched last week is approximately **10.705 hours**.

Rounding to the nearest thousandth, the answer is:

\[
\boxed{10.705}
\] hours.