Step 3: Sampling distribution is df =n-2=30-2=28.

Step 4: Decision Rule: I will reject Ho if the value of the Pearson Product Moment Correlation, r, is less than the negative or greater than the positive critical value that will be obtained from the t-tables, otherwise, I will fail to reject.

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Step 5: Calculation:

The Pearson Product Moment Correlation, r = 0.5341.

The Critical value from the t-table =2.05.

Step 6: Summary: Since the calculated r is in between the positive and the negative values of the critical value from the t-tables, I fail to reject Ho.

Step 7: Conclusion: Since the Ho was not rejected, I conclude that the Pearson Product Moment Correlation is not significantly different from zero and, therefore, the correlation line between the height and weight may not be used for prediction of the values of the dependent variable.

Problem 2 - Weight vs. Age

Step 1:

Ho: The Pearson Product Moment Correlation is not significantly different from zero.

Ha: The Pearson Product Moment Correlation is significantly different from zero.

Step 2: Alpha level, =Two sided 0.01.

Step 3: Sampling distribution is df =n-2=30-2=28.

Step 4: Decision Rule: I will reject Ho if the value of the Pearson Product Moment Correlation, r, is less than the negative or greater than the positive critical value that will be obtained from the t-tables, otherwise, I will fail to reject.

Step 5: Calculation:

The Pearson Product Moment Correlation, r = 0.110044.

The Critical value from the t-table =2.76.

Step 6: Summary: Since the calculated r is in between the positive and the negative values of the critical value from the t-tables, I fail to reject Ho.

Step 7: Conclusion: Since the Ho was not rejected, I conclude that the Pearson Product Moment Correlation is not significantly different from zero and, therefore, the correlation line between the weight and age may not be used for prediction of the values of the dependent variable.

Problem 3 - Height vs. Shoe Size

Step 1:

Ho: The Pearson Product Moment Correlation is not significantly different from zero.

Ha: The Pearson Product Moment Correlation is significantly different from zero.

Step 2: Alpha level, =Two sided 0.02.

Step 3: Sampling distribution is df =n-2=30-2=28.

Step 4: Decision Rule: I will reject Ho if the value of the Pearson Product Moment Correlation, r, is less than the negative or greater than the positive critical value that will be obtained from the t-tables, otherwise, I will fail to reject.

Step 5: Calculation:

The Pearson Product Moment Correlation, r = 0.5509.

The Critical value from the t-table =2.47.

Step 6: Summary: Since the calculated r is in between the positive and the negative values of the critical value from the t-tables, I fail to reject Ho.

Step 7: Conclusion: Since the Ho was not rejected, I conclude that the Pearson Product Moment Correlation is not significantly different from zero and, therefore, the correlation line between the height and shoe size may not be used for prediction of the values of the dependent variable.

Question 2 - Explain the Correlation Coefficient of Determination

The correlation coefficient of determination is the square of the Pearson's Moment Product Coefficient, denoted as r2. It only assumes values between 0 and 1. Generally for two variables x and y, the value of r2 can be calculated as:

r2=nxy-xynx2-x2ny2-y22 where x and y are the variables, n is the number of observations and r2 is the correlation coefficient of determination.

It gives the proportion of the change or variance in the dependent variable that can be probable from the independent variable. If the value of r2=0, it means that no prediction can be done on the value of the dependent variable given the value of the independent variable whereas if r2=1, the value of the dependent variable can be predicted perfectly without any error, given the value of inthe dependent variable. Otherwise, a value in between 0 and 1 gives the level of predictability of the dependent variable given the independent variable. For instance, a value r2=0.35 means that only a shift of 35 per cent in the values of the dependent variable can be accounted for by the independent variable.