Multiple Linear Regression

class: center, middle, inverse, title-slide

.title[
# Multiple Linear Regression
]
.subtitle[
## Concerning Expenses for Farmers
]
.author[
### Connor McKee
]
.institute[
### West Chester University
]
.date[
### 02-15-2023
]

---

## The research/practical questions
The annual expenses of various livestock markets were monitored. How do these depend on the number of animals sold?

## Description of data
This is a data set contains the annual expenses of various livestock markets that were monitored. It contains 19 observations with 7 variables. The variables include:

---

.pull-left[

## Variable
- I
- one
- cattle
- calves
- pigs
- lambs
- expenses
]

.pull-right[

## Description
- the index (nominal)
- 1 (categorical)
- Cattle in thousands (numerical)
- Calves in thousands (numerical)
- Pigs in thousands (numerical)
- lambs in thousands (numerical)
- expenses in thousands of dollars (numerical)
]

---

## Model and Diagnostics

```r
farmers = read.table("https://people.sc.fsu.edu/~jburkardt/datasets/regression/x19.txt", skip=41)
          #above I read a text file in and skipped 41 lines which described the data set

names(farmers) = c("Index", "one", "cattle", "calves", "pigs", "lambs", "expenses")
                                         #above I named the variables
farmers[8,7] = 14.755                    #was a missing value because of a comma
expenses = as.numeric(farmers$expenses)  #made expenses variable numerical value
cattle = farmers$cattle                  #made all numeric values objects 
calves = farmers$calves              
pigs = farmers$pigs
lambs = farmers$lambs
#made new data set with numerical values, I left out variables Index and one.
finalfarmers = data.frame(expenses, cattle, calves, pigs, lambs) 
```

---

## Building Model

```
## 
## Call:
## lm(formula = expenses ~ ., data = finalfarmers)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.3588 -3.9668  0.4735  2.6222 12.0169 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   2.2831     3.3832   0.675 0.510781    
*## cattle        3.2078     0.4221   7.600 2.48e-06 ***
## calves        1.6191     0.8508   1.903 0.077819 .  
## pigs          0.8168     0.4699   1.738 0.104123    
*## lambs         0.8048     0.1899   4.238 0.000828 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.151 on 14 degrees of freedom
*## Multiple R-squared:  0.9374,    Adjusted R-squared:  0.9196 
*## F-statistic: 52.45 on 4 and 14 DF,  p-value: 2.834e-08
```

---

```r
knitr::include_graphics('./Assignment2Picture.png')
```

---

## Final Model

`$$expenses=2.2831+3.2078(cattle)+1.6191(calves)$$`
              `$$+0.8168(pigs)+0.8048(lambs)$$`

## Conclusion
In conclusion, we see that cattle are the most expensive animal to buy. For every 1000 cattle bought, expenses increase by $3,207.80. Lambs are the least expensive animal to buy. For every 1000 lambs bought, expenses increase by $804.80.