Question

Have you ever noticed that adults like the taste of some bitter foods that adolescents just cannot tolerate the taste of? Things like dark chocolate, grapefruit, coffee, etc. Ms. Wilson is interested in whether bitter flavors become more tolerable as people get older. She sets up a study in which subjects taste cups of coffee that are different strengths and picks their favorite one.

Ms. Wilson records the age of each subject, x, and the strength of the coffee in grams, y, that the subject liked the best.

Age of Subject Strength of Coffee in grams
17 48
27 44
33 49
37 54
40 57


(4 points)
Use the Desmos Graphing Calculator (right-click and open in new tab/window) to calculate the following:

r =
0.7343

y =
0.413
x +
37.684

If someone was 45 years old, what would the regression line predict for the strength of coffee they would prefer?

Answer 1

To predict the strength of coffee preferred by a 45-year-old using the regression line equation given, we can substitute \( x = 45 \) into the equation:

\[
y = 0.413x + 37.684
\]

Now replacing \( x \) with 45:

\[
y = 0.413(45) + 37.684
\]

Calculating the multiplication:

\[
y = 18.585 + 37.684
\]

Now adding those two values together:

\[
y = 56.269
\]

Therefore, the regression line predicts that a 45-year-old would prefer a coffee strength of approximately **56.27 grams**.