Predicting the Unknown

Multi regression is a statistical technique used to find the relationship between multiple independent variables (predictors) and output variable (dependent variable), and determine how each IV influence the DV. The Weights of those IVs can be quantified using a multiple regression model that has the below form

Y = a + b1X1 + b2X2+b3X3…..+bnXn

Where Y is the DV, X1,X2,X3,…..,Xn are the IV or predictors, a is the intercept, and b1….bn are the weights of the IV.

Now let go through the process of creating a multi-regression model in R. The data used is from PSY530 (SPSS). In this example we will use a set of anthropometric data collected on 25 males and determine which of these variables better predict height in males. The data collected include measurement such as left foot, right foot, left arm, right arm…etc

Step1:

Let’s start by hypnotizing that all these variable will have the same influence on the predictability of height, so our model will look like this:

fit1<lm(Height~LeftArm+RtArm+LeftFoot+RtFoot+LeftHand+RtHand+HeadCirc,data=HeightMales)

Summary (fit1)

After running this model in R will get the following data:

The regression analysis performed on the male height indicated that the predictors explained 58.36% of the data. But looking closely at the coefficients we see left arm and left foot has the most influence on the prediction of height.

Step2:

Now we run our analysis with only the data from left foot and left arm

fit2<-lm(Height~LeftArm+LeftFoot,data=HeightMales)

summary(fit2)

Running the above code in R will produce the following results:

Looking at the results closely we see that 52.68 of data is explained by our model with only two independent variables (left foot and left arm). Left foot being the most predictor for height in men (explaining 87.58 % of the data).

Step3:

Now we could predict height in men by creating a multi regression equation using the coefficients for the left foot, left arm and intercept as follow:

Height= 27.2864+0.7519*LeftArm+0.8758*LeftFoot

Play with this equation by replacing values for LeftArm and LeftFoot and see the results.

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