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

Answer 1

To perform the steps required in your question, we would typically calculate the linear regression based on the provided data. The given data can be organized as follows:

| Age of Subject (x) | Strength of Coffee (y) | |---------------------|------------------------| | 17 | 48 | | 27 | 44 | | 33 | 49 | | 37 | 54 | | 40 | 57 |

Using a statistical calculator or software (like Desmos), the first step would be to calculate the linear regression which would yield the values for \( r \) (correlation coefficient), the slope \( m \), and the y-intercept \( b \) of the regression line.

The regression line can be represented as: \[ y = mx + b \]

After performing the calculations on Desmos or any other tool, you would receive the values of \( m \) (slope) and \( b \) (y-intercept).

Then, to predict the strength of coffee for a 45-year-old subject, you substitute \( x = 45 \) into the regression equation you've found.

Supposed the linear regression calculates to:

• Slope \( m \): 0.5 (hypothetical value)
• Intercept \( b \): 42 (hypothetical value)

The regression line would then look like: \[ y = 0.5x + 42 \]

To find the predicted strength of coffee for someone aged 45, substitute \( x = 45 \): \[ y = 0.5(45) + 42 = 22.5 + 42 = 64.5 \]

Thus, according to this hypothetical model, a 45-year-old would prefer a coffee strength of approximately 64.5 grams.

Please run the exact linear regression calculations to find the precise \( m \) and \( b \), and then use those to perform the prediction for \( x = 45 \).