Question

Brendan is a programmer in Silicon Valley and spends most of his day typing and drinking coffee. He wants to know if drinking coffee makes him type faster.
Over the next few days, Brendan varies the number of cups of coffee he drinks, x, and measures the average number of words typed per minute on each day, y.
The least squares regression line of this data set is:
y=0.938x+84.434
What average daily typing speed does this line predict if Brendan drinks 3.28 cups of coffee?
Round your answer to the nearest thousandth.

Answer 1

To predict Brendan's average daily typing speed based on the number of cups of coffee he drinks, we can use the least squares regression line equation:

\[
y = 0.938x + 84.434
\]

Here \(x\) represents the number of cups of coffee, and \(y\) represents the average number of words typed per minute.

To find the predicted typing speed when \(x = 3.28\), we substitute \(3.28\) for \(x\) in the equation:

\[
y = 0.938(3.28) + 84.434
\]

Now, calculate \(0.938 \times 3.28\):

\[
0.938 \times 3.28 = 3.07584
\]

Next, add \(84.434\):

\[
y = 3.07584 + 84.434 = 87.50984
\]

Rounding this to the nearest thousandth, we get:

\[
y \approx 87.510
\]

Thus, the predicted average daily typing speed if Brendan drinks 3.28 cups of coffee is **87.510** words per minute.