A statistical method you can use to understand the relationship of two variables, x and y.

• X is known as the predictor variable
• Y is known as the response variable

Why is this useful:

• establishes trends
• makes predictions
• shows how variables affect each other

The data set used for this analysis is the iris dataset.

• X (predictor): petal length
  
• Y (response): petal width

We will use linear regression to examine the relationship between these two variables.

The formulas below show the theoretical equation and the fitted regression equation.

Theoretical model:

\[ Y = \beta_0 + \beta_1 X + \epsilon \] - \(\beta_0\): intercept
- \(\beta_1\): slope
- \(\epsilon\): error term

Fitted model:

\[ \hat{y} = \hat{\beta}_0 + \hat{\beta}_1 x \] This is also referred to as the prediction equation

The graph shows a strong relationship between petal length and width, as indicated by the regression line.

The graph shows a weak relationship between length and width because of the scattered points.

## 
## Call:
## lm(formula = Petal.Width ~ Petal.Length, data = iris)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.56515 -0.12358 -0.01898  0.13288  0.64272 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.363076   0.039762  -9.131  4.7e-16 ***
## Petal.Length  0.415755   0.009582  43.387  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2065 on 148 degrees of freedom
## Multiple R-squared:  0.9271, Adjusted R-squared:  0.9266 
## F-statistic:  1882 on 1 and 148 DF,  p-value: < 2.2e-16