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
r =
y =
x +
If someone was 45 years old, what would the regression line predict for the strength of coffee they would prefer?
To find the predicted strength of coffee for someone who is 45 years old, we can first calculate the regression line using the data provided.
First, we need to calculate the mean values for x and y:
Mean of x (age) = (17 + 27 + 33 + 37 + 40) / 5 = 30.8
Mean of y (strength of coffee) = (48 + 44 + 49 + 54 + 57) / 5 = 50.4
Next, calculate the sums of squares:
Σ(x - x̅)(y - y̅) = (17-30.8)(48-50.4) + (27-30.8)(44-50.4) + (33-30.8)(49-50.4) + (37-30.8)(54-50.4) + (40-30.8)(57-50.4) = -31.2
Σ(x - x̅)² = (17-30.8)² + (27-30.8)² + (33-30.8)² + (37-30.8)² + (40-30.8)² = 436.8
Calculate the slope of the regression line (b):
b = Σ(x - x̅)(y - y̅) / Σ(x - x̅)² = -31.2 / 436.8 ≈ -0.0715
Now we can calculate the intercept (a):
a = y̅ - b(x̅) = 50.4 - (-0.0715)(30.8) ≈ 52.79
Therefore, the regression line equation is y = -0.0715x + 52.79
To find the predicted strength of coffee for someone who is 45 years old:
y = -0.0715(45) + 52.79 ≈ 49.17
The regression line predicts that someone who is 45 years old would prefer a coffee strength of approximately 49.17 grams.