Question

The National Football League has performed a study in which the total yards gained by teams in games was used as an independent variable to explain the variation in total points scored by teams during games. The points scored ranged from 0 to 57 and the yards gained ranged from 187 to 569. The following regression model was determined: = 12.3 + .12x. Given this model, which of the following statements is true?

A. For every one point scored, the predicted number of yards gained increased by 0.12, on average.
B. For every one yard gained, the predicted number of points increased by 0.12, on average.
C. For every one yard gained, the predicted number of points scored decreased by 12.3, on average.
D. For every one point scored, the predicted number of points scored, decreased by 12.3, on average.

Answer 1

Answer:

A. For every one point scored, the predicted number of yards gained increased by 0.12, on average.

That's not correct, what we have that for each yard gained by the temas we have an increase of 0.12 of points scored.

B. For every one yard gained, the predicted number of points increased by 0.12, on average.

That's correct and is the interpretation for the slope on this case.

C. For every one yard gained, the predicted number of points scored decreased by 12.3, on average.

That's not true the correct interpretation for the intercept is that the points for a team that gain 0 yards it's on average 12.3 points.

D. For every one point scored, the predicted number of points scored, decreased by 12.3, on average.

That's not true the correct interpretation for the intercept is that the points for a team that gain 0 yards it's on average 12.3 points.

Step-by-step explanation:

Some notation

x represent the variable "total yards gained by teams in games " and the possible values for x are between 187 to 569

y represent the variable "total points scored by teams" and the possible values for y are between 0 to 57

We conduct a linear regression model in order to explian the variable y in terms of the variable x.

Solution to the problem

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

And the slope would be:

$m=0.12$

And we can find the intercept using this:

$b=\bar y -m \bar x=12.3$

So the line would be given by:

$y=0.12 x +12.3$

And that was the output provided. Now we need to analyze the following statements:

A. For every one point scored, the predicted number of yards gained increased by 0.12, on average.

That's not correct, what we have that for each yard gained by the temas we have an increase of 0.12 of points scored.

B. For every one yard gained, the predicted number of points increased by 0.12, on average.

That's correct and is the interpretation for the slope on this case.

C. For every one yard gained, the predicted number of points scored decreased by 12.3, on average.

That's not true the correct interpretation for the intercept is that the points for a team that gain 0 yards it's on average 12.3 points.

D. For every one point scored, the predicted number of points scored, decreased by 12.3, on average.

That's not true the correct interpretation for the intercept is that the points for a team that gain 0 yards it's on average 12.3 points.