Linear Regression

Quality rating, customer satisfaction

Quality rating, customer satisfaction

The quality rating impacts the customer satisfaction

Associative Forecasting

Used when changes in one or more independent variables can be used to predict the changes in the dependent variable

For Associative forecasting, the most common technique is

linear regression analysis

A statistical model estimates how

variables relate to one another

Regression is a statistical model that uses one or more

independent variables to predict a dependent variable

Regression is an

Outcome based on predictor variables by using the least squares technique

Outcome (dependent variable)

Y variable

Predictor variables

x variable (Independent variable)

Least square technique

Line of best fit

b

slope of the regression

a

y-axis intercept

Regression estimates the

Line of best fir or the line tat passes closest to points in a scatter plot

The correlation coefficient, R, indicates how closet our line of best fit models to the

how closet our line of best fit models to the data

R ranges from

-1 to +1

When R = 0 there is not a

clear relationship between X and Y

The Coefficient of determination measures how

how well a statistical model predicts an outcome/the goodness of fit of a regression model

What does the coefficient of determination represent?

The proportion of variance in the dependent variable that is predictable from the independent variables in a regression model

R squared can be used to evaluate and compare

different regression models

If R2 = .6 it means 60% of the variation in the output variable is predictable by the input variables OR

60% of the values fir the model

The closer the R-Squared is close to 1, the better the model fits the data because

it explains a larger proportion of the variability in the dependent variable

A low R squared suggests

the model does not explain much of the variation in the dependent variable, indicating that it may not be a good fit

R measures the

Strength and direction of the linear relatiosnhip between two variables.

R squared is the square of the

Correlation coefficient (r )

R-Squared quantifies how well a regression model fits the data and explains the proportion of

variance in the dependent variable that is predictable from the independent variable in a regression model

R2 provides information about the

model’s goodness of fit and predictive power

R primarily assesses the

linear association between two variables

Carat example x and y

The heavier the carat weight (x) the higher the price will be (y)

R= .84 R2 = .7 interpretation

“70% variation on the price of a diamond is explained by changes on carat rate”

The value multiplied by x is

Slop coefficient

y = -1027.77 + 4318.79x

for each additional change on the carat rate we expect the diamond price to go up by 4318 dollars on average

Y = -1027.77 + 4318.79x , if this diamond is price at $2,800 is it a good deal or not?

No, because when you plug in .8 its worth 2427

y = -1027.77 + 4318.79x, what is x?

Carat Weight

Residuals are the

difference between the observed actual y values and predicted y values

Residual formula

observed value - Predicted value

Coefficient Estimate for y=1.75 + 25x

For each unit increase on x, you expect y increases by .25 units on average

what is x in this example y=1.75 + 25x

Payroll

if p value is less than .05 it is

variably statistical