Homework #1 Correlation Calculation and Interpretation Directions: Step 1: Draw a scatterplot to represent the X and Y. Calculate the sum of the crossproducts conceptually. Calculate Pearson r using...

Solution of Homework #1
· Scatter Plot of X and Y:
· Calculation of Sum of Cross – Products:
The formula for calculating Sum of Cross – Product is as follows:
The following table shows the calculation of the sum of cross – products.
· Calculation of Pearson’s Correlation Coefficient (r):
The formula of calculating Pearson’s Correlation Coefficient is as follows:
The following table shows the calculation of Pearson’s Correlation Coefficient (r)
· If, X = Attitude, and, Y = Productivity, then Interpretation of r:
From the above value of r, if X = Attitude and Y = Productivity, then it can be explained as there is no relation between one’ attitude and productivity as the Pearson’s Correlation Coefficient is very low (nearly, 0.1). Since, the sample size is very small, let’s look at the effect size of X and Y and it is 1.273763. From the above scatter plot, it can be seen that X and Y have a positive direction of association but the strength of association is very week.
· Value of r2 and 1 – r2:
The following table shows the values of r, r2 and 1 – r2.
    r
    0.12375
    r2
    0.01531
    1 – r2
    0.98469
From the value of r2, one can infer that proportion of variance explained by X, to predict Y is 1.5%, which is very low. On the other hand, the value of 1 – r2, shows that the proportion of variance is unexplained in the variable X to predict Y is 98.5%.
· Venn Diagrams to explain the Coefficient of Determination and Non-Determination:
In the above figure, the left circle represents the X variable (Predictor Variable) and the right circle represents the Y variable (Response Variable). The Coefficient of Determination is the explained variation of the response variable in the predictor variable, which is here represented by the Blue Area, and...