Question

1. the scatter - plot shows the number of annual scholarly publications on the topic of artificial intelligence (ai) where x is the number of years since 2010 and y is the number of publications.

a. describe the relationship between the years and the number of publications.
b. a linear regression model for these data is calculated. the residual plot is shown. is the linear model a good fit for these data? explain.
c. it is suspected that the data follows more of an exponential pattern. suppose we transformed the data so that the response variable is the log of the annual number of publications. predict what you think the scatter - plot will look like.
d. the equation for the new regression line for the transformed data is log(annual number of publications)=5.2096 + 0.0402(years since 2010). use this model to predict the annual number of scholarly publications on the topic of ai in 2019, to the nearest publication.

Explanation:

Step1: Determine the value of x for 2019

Since x is the number of years since 2010, for 2019, $x = 2019 - 2010=9$.

Step2: Substitute x into the regression - line equation

The regression - line equation is $\log(\text{annual number of publications})=5.2096 + 0.0402x$. Substitute $x = 9$ into the equation:
$\log(\text{annual number of publications})=5.2096+0.0402\times9$
$=5.2096 + 0.3618$
$=5.5714$.

Step3: Solve for the annual number of publications

If $\log(y)=5.5714$ (where y is the annual number of publications), then $y = 10^{5.5714}$.
Using a calculator, $y\approx372394$.

Answer:

372394