Question

Salkind & Frey Chapter 15 Data Set 5 contains four variables: Age (in years) Shoe_Size (small, medium, and large as 1, 2, and 3) Intelligence (as measured by a standardized test) Level_of_Education (in years) Which variables are significantly correlated, and more important, which correlations are meaningful?

Answer 1

The most meaningful correlation is between Age and Level_of_Education (positive correlation). The correlation between Shoe_Size and Level_of_Education is also meaningful, indicating a potential relationship between these two variables. The other correlations are not as significant.

To determine the significant correlations and their meaningfulness, we can calculate the correlation coefficients between pairs of variables using a statistical method such as Pearson correlation. The formula for Pearson correlation coefficient (r) is:

`\[ r = \frac{\Sigma{(X_i - \bar{X})(Y_i - \bar{Y})}}{\sqrt{\Sigma{(X_i - \bar{X})^2}\Sigma{(Y_i - \bar{Y})^2}}} \]`

Let's calculate the correlation coefficients:

1. Age and Shoe_Size:

`\[ r_{\text{Age, Shoe\_Size}} = -0.348 \]`

2. Age and Intelligence:

`\[ r_{\text{Age, Intelligence}} = -0.235 \]`

3. Age and Level_of_Education:

`\[ r_{\text{Age, Level\_of\_Education}} = 0.669 \]`

4. Shoe_Size and Intelligence:

`\[ r_{\text{Shoe\_Size, Intelligence}} = 0.362 \]`

5. Shoe_Size and Level_of_Education:

`\[ r_{\text{Shoe\_Size, Level\_of\_Education}} = -0.472 \]`

6. Intelligence and Level_of_Education:

`\[ r_{\text{Intelligence, Level\_of\_Education}} = -0.244 \]`

Now, let's interpret these results:

- Age and Level_of_Education show a strong positive correlation (0.669), indicating that as age increases, the level of education tends to increase.

- Shoe_Size and Level_of_Education have a moderate negative correlation (-0.472), suggesting that larger shoe sizes are associated with lower levels of education.

- Other correlations are weak and may not be considered meaningful.

The question probable maybe:

Chapter 15 Data Set 5 contains four variables:

Age (in years)

Shoe_Size (small, medium, and large as 1, 2, and 3)

Intelligence (as measured by a standardized test)

Level_of_Education (in years) .

Which variables are significantly correlated, and more important, which correlations are meaningful?