# Problem 1

PLease Use R while solving these problems

The file called `football.csv` available on blackboard is a dataset that contains 28 observations from the 1976 season of the NFL.

football <- read.csv("https://raw.githubusercontent.com/kshoemaker/Class_test/master/football.csv",

header = T, row.names = 1)

## Part (a)

An analyst suspects there is a relationship between `GamesWon`, the number of games won in a season, and `PassYds`, passing yards, `PctRush`, percent of rushing plays, and `OppRushYds`, the opponents rushing yards. For now, we work with only these three variables. Build an MLR model to predict `GamesWon` using the other three variables.

Considering only the information in `summary()`, assess the *significance* of the model.

## Part (b)

Using other diagnostic tools that we have learned, assess the *validity* of the assumptions of the model.

## Part (c)

Consider performing a partial F test to test for the inclusion of `PctRush` in the model. Either in words or formula, what are the null and alternative hypotheses for this test?

## Part (d)

Compute the test you considered in part (c). What is your conclusion at a 5% significance level? What is your conclusion at a 1% significance level? State both conclusions in full sentences.

## Part (e)

Compute the variance inflation factors of the three coefficients. Is there any cause for concern?

(f)

Using the model with all three predictors, estimate how many more games per season a team will win if they are able to increase their passing yardagefor the season (`PassYds`) by 300, all other things remaining equal.

Part (g)

Suppose we had to cancel the 1977 season for some crazy reason like a global pandemic. We want to estimate the wins for the 1977 season by using the 1976 data. How many teams have more [predicted/extrapolated/estimated] wins for the 1977 season than wins in the 1976 season? How many have less? How many have the same?