Now we will fit our first regression model.
The command to do this is lm() e.g. linear model.
output <- lm(y_column ~ x_column,data=tablename)
outputNOTE, THE WEIRD ~ SYMBOL. This means “depends on”/“is modelled by” and it’s how we tell R what the response variable is. E.g. in y=mx+c, y depends on x, or y is modelled/predicted by x.
For example for the NYHouses dataset, if I wanted to create a model of the Price and Lot columns to see if Lot size could predict house sales price, then I would type.
# response = Price, predictor = Lot size
Model1.lm <- lm(Price ~ Lot,data=HousesNY)
Model1.lm##
## Call:
## lm(formula = Price ~ Lot, data = HousesNY)
##
## Coefficients:
## (Intercept) Lot
## 114.0911 -0.5749So we are saying here that the equation is
Expected_Average_Price = -0.5749*Lot_Size + 114.0911
E.g. the average expected price house with no Lot/Garden is 114.09 (x1000 USD)
Now you have the numbers, you can use Tutorial 6 on Markdown to print out the equation. For example, if you wanted to print out the equation of the line, you could use the following code:
\[ \hat{y} = 114.0911 -0.5749 \times \text{Lot} \]
You can look at the summary by using the summary()
command:
summary(Model1.lm)##
## Call:
## lm(formula = Price ~ Lot, data = HousesNY)
##
## Residuals:
## Min 1Q Median 3Q Max
## -74.775 -30.201 -5.941 27.070 83.984
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 114.0911 8.3639 13.641 <2e-16 ***
## Lot -0.5749 7.6113 -0.076 0.94
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 41.83 on 51 degrees of freedom
## Multiple R-squared: 0.0001119, Adjusted R-squared: -0.01949
## F-statistic: 0.005705 on 1 and 51 DF, p-value: 0.9401If you want a different way of seeing the same output, you can use
the ols_regress() command inside the olsrr
package. THIS ONLY WORKS IF YOU USED lm(y ~ x, data=TABLENAME). If you
used a $ it will break.
library(olsrr)
Model1.lm.ols <- ols_regress(Model1.lm)
Model1.lm.ols## Model Summary
## -----------------------------------------------------------------
## R 0.011 RMSE 41.035
## R-Squared 0.000 MSE 1683.876
## Adj. R-Squared -0.019 Coef. Var 36.813
## Pred R-Squared -0.068 AIC 550.137
## MAE 34.152 SBC 556.048
## -----------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
## AIC: Akaike Information Criteria
## SBC: Schwarz Bayesian Criteria
##
## ANOVA
## --------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## --------------------------------------------------------------------
## Regression 9.983 1 9.983 0.006 0.9401
## Residual 89245.412 51 1749.910
## Total 89255.395 52
## --------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------
## (Intercept) 114.091 8.364 13.641 0.000 97.300 130.882
## Lot -0.575 7.611 -0.011 -0.076 0.940 -15.855 14.705
## -------------------------------------------------------------------------------------------The ols_regress command produces beautiful output, but sometimes it doesn’t work well with other commands. So I tend to run a lm command at the same time to have both available.
See the scatterplot tutorial under plots!