Question

question 9
a soft drink company is launched an advertising campaign and they’re tracking the number of visits to their website in the months following the launch. the graph shows the number of visits based on the months after the campaign’s launch. the advertising team fit the data with a linear regression that has a ( r^2 ) value of 0.88.

is this linear function a good model for the data?

a. yes, there is a strong correlation, and the data points decrease approximately by a constant ratio.
b. yes, this is a moderate correlation, and the data points decrease by a constant rate.
c. no, there is a moderate correlation, and an exponential function would be a better fit for the data.
d. no, although this is strong model, a logistic model would be a better fit for the data.

graph: ( f(x) = -0.69x + 8.55 ), ( r^2 = 0.88 ), with data points plotted

Explanation:

1. Recall the meaning of \( r^2 \) (coefficient of determination): Values close to 1 (e.g., 0.88) indicate a strong linear relationship between the variables.
2. Analyze the options:

• Option A: Incorrect. A constant ratio implies exponential decay, but the model is linear (constant rate of change, not ratio).
• Option B: Incorrect. \( r^2 = 0.88 \) is a strong, not moderate, correlation.
• Option C: Incorrect. \( r^2 = 0.88 \) is strong, and the data does not suggest an exponential fit (exponential decay would show a curve with changing rates, but the linear model already has a strong fit).
• Option D: Correct. The \( r^2 = 0.88 \) shows a strong linear fit, but the data (visits over time) may follow a logistic pattern (e.g., initial decline, then stabilizing), making a logistic model more appropriate for long - term behavior.

Answer:

D. No, although this is strong model, a logistic model would be a better fit for the data.