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# 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...

Homework #1
Co
elation 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 the computational formula.
Step 2: If X = Attitude and Y = Productivity, interpret r. More specifically, write a sentence explaining the effect size for X and Y, and a sentence indicating the directionality and strength of association between X and Y. Calculate r2 and 1 â€“ r2. Draw and label a venn diagram to illustrate the coefficient of determination and coefficient of non-determination. Write a sentence which interprets each coefficient.
Student    X    Y
1    23    34
2    20    31
3    24    30
4    17    30
5    16    35
6    23    30
7    21    34
8    20    33
9    25    39
10    24    31
Answered Same Day Jun 10, 2021

## Solution

Solution of Homework #1
Â· Scatter Plot of X and Y:
Â· Calculation of Sum of Cross â€“ Products:
The formula for calculating Sum of Cross â€“ Product is as follows:
The following table shows the calculation of the sum of cross â€“ products.
Â· Calculation of Pearsonâ€™s Co
elation Coefficient (r):
The formula of calculating Pearsonâ€™s Co
elation Coefficient is as follows:
The following table shows the calculation of Pearsonâ€™s Co
elation Coefficient (r)
Â· 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 oneâ€™ attitude and productivity as the Pearsonâ€™s Co
elation Coefficient is very low (nearly, 0.1). Since, the sample size is very small, letâ€™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.
Â· Value of r2 and 1 â€“ r2:
The following table shows the values of r, r2 and 1 â€“ r2.

0.12375
r2
0.01531
1 â€“ 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 â€“ r2, shows that the proportion of variance is unexplained in the variable X to predict Y is 98.5%.
Â· 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...
SOLUTION.PDF