Question

Jonas runs a channel where he uploads and shares videos that he makes. He noticed an exponential relationship between how long his videos have been posted and the number of times each video has been viewed.
Jonas took the natural logarithm for the numbers of views only, and he noticed a linear relationship between the how long his videos have been posted and the transformed numbers of views.
Here's the least-squares regression equation for the transformed data, where "time" represents days since posting, and "views" is the number of views.
\widehat{\ln(\text{views})}=0.77(\text{time})+2.90
ln(views)
​
=0.77(time)+2.90
According to this model, what is the predicted number of views on a video that's been posted for 222 days?

Answer 1

Answer:

The predicted number of views on a video that's been posted for 222 days is approximately 3.1459567 × 10⁷⁵ views

Explanation:

$\widehat{\ln(\text{views})}=0.77(\text{time})+2.90$

The given parameters for the exponential relationship between the number of views and the duration after posting a video is presented as follows;

$\widehat {\ln{(views)}} = 0.77 \times \text{time} + 2.90$

For a video that has been posted 222 days, we have;

Time = 222 days

Therefore, we get;

ln(views) = 0.77 × 222 + 2.90 = 173.84

∴ The predicted number of views on a video that's been posted for 222 days = e^173.84 = 3.1459567 × 10⁷⁵