Question

1. taylor swift created a video and posted it on her instagram account. taylor’s media personnel collected the number of views the video had after every hour. use the data to answer the following questions.

a) what model would best be used to represent this data? linear, quadratic, or exponential?
b) use the regression capabilities on your calculator to find the model chosen above for the height of a person, h(x), given their shoe size, x.
c) use the model found in part b to predict the number of views the video had after 1 day.
d) the actual number of views after one day was 6 million. what is the residual for this number of views? did the model overestimate or underestimate the number of views?

1. if a function is a good model of a set of data, describe and graph what the residual plot should look like.

hours | # of views
1 | 50
3 | 182
5 | 613
6 | 1489
8 | 7200
10 | 30,957

Explanation:

Part d)

Step 1: Recall Residual Formula

Residual \( R \) is calculated as \( R = \text{Actual} - \text{Predicted} \). The actual views are \( 6,000,000 \) and the predicted views from part c) are \( 685904823.7 \).

Step 2: Calculate Residual

Substitute the values into the formula:
\( R = 6,000,000 - 685,904,823.7 \)
\( R = -679,904,823.7 \)

Step 3: Determine Over/Underestimate

Since the predicted value (\( 685,904,823.7 \)) is greater than the actual value (\( 6,000,000 \)), the model overestimated the number of views.

A good model’s residual plot should have residuals randomly scattered (no pattern) around \( y = 0 \), with no clustering, trends (increasing/decreasing), or curvature. The residuals’ spread (variance) should be constant (homoscedastic). Visually, points are dispersed evenly above and below the horizontal axis (\( y = 0 \)) without forming lines, curves, or clusters.

Answer:

The residual is \( -679904823.7 \), and the model overestimated the number of views.

Part 17)