Question
Caleb is a psychology professor studying the effect of media violence on modern culture. As part of his research, he analyzed the content of several recent action movies.
For each movie, he noted the running time (in minutes), x, and the number of explosions, y.
The least squares regression line of this data set is:
y=0.628x–63.411
How many explosions does this line predict would be in a 150 minute action movie?
Round your answer to the nearest integer.
explosions
For each movie, he noted the running time (in minutes), x, and the number of explosions, y.
The least squares regression line of this data set is:
y=0.628x–63.411
How many explosions does this line predict would be in a 150 minute action movie?
Round your answer to the nearest integer.
explosions
Answers
Answered by
GPT-4o mini
To predict the number of explosions in a 150-minute action movie using the least squares regression line \( y = 0.628x - 63.411 \), we substitute \( x = 150 \) into the equation.
\[
y = 0.628(150) - 63.411
\]
First, calculate \( 0.628 \times 150 \):
\[
0.628 \times 150 = 94.2
\]
Next, substitute this value back into the equation:
\[
y = 94.2 - 63.411
\]
Now, perform the subtraction:
\[
y = 30.789
\]
Finally, rounding to the nearest integer, we get:
\[
\text{Predicted number of explosions} = 31
\]
Thus, the line predicts that a 150-minute action movie would have approximately **31 explosions**.
\[
y = 0.628(150) - 63.411
\]
First, calculate \( 0.628 \times 150 \):
\[
0.628 \times 150 = 94.2
\]
Next, substitute this value back into the equation:
\[
y = 94.2 - 63.411
\]
Now, perform the subtraction:
\[
y = 30.789
\]
Finally, rounding to the nearest integer, we get:
\[
\text{Predicted number of explosions} = 31
\]
Thus, the line predicts that a 150-minute action movie would have approximately **31 explosions**.