Step 1: Calculate the least squares regression equation using mother's schooling (X) to predict family income (Y).

Example: P = 42.21 + 0.52x

Step 2: Use your prediction equation from Step 1 to predict the family income for a patient whose mother completed 16 years of schooling.

Step 3: Calculate the total sum of squares (SST), residual sum of squares (SSE), and regression sum of squares (SSR).

Step 4: Calculate the F statistic. Is it statistically significant at a level of significance of 0.05?

Step 5: Calculate the coefficient of determination (R²). Write a sentence that interprets the coefficient of determination using the variables of the problem (mother's years of schooling and family income).

Data:

- Mother's highest year of schooling completed:
8, 12, 18, 12, 18, 19, 20, 20, 16, 16, 13, 18, 19, 20, 22, 12, 10, 19, 20, 13, 18, 10, 10

- Family income (in thousands of dollars):
33.0, 53.0, 70.8, 88.0, 60.4, 90.5, 100.2, 72.2, 57.0, 79.0, 41.1, 68.8, 55.5, 60.9, 72.9, 18.8, 16.5, 86.4, 68.5, 2.2, 71.1, 26.8, 22.2

Gina Sullivan, a researcher in healthcare economics, hopes to predict each patient's family income (and therefore ability to pay) based on the mother's highest level of education.

For example, "12" means that the mother completed 12 years of schooling (high school graduate). To help keep the numbers manageable, income is rounded. For example, 21.8 means the family income was $21,800.

Gina looked at historical data from 20 previous patients.

The researcher predicts a circle of profits from the usage of the mother's training. Calculated regression equation expected income for 16 years of schooling and analyzed version significance using F-statistic and [tex]R^2[/tex].

In this hassle, the researcher's objective is to expect own family earnings based on the mom's maximum level of schooling. The first step entails finding the least squares regression equation, which enables the model of the relationship between training (X) and circle of relatives profits (Y). Using ancient facts from 20 patients, the regression equation is determined.

Next, the prediction equation is used to estimate the family profits for an affected person whose mom completed 16 years of schooling. This provides a man or woman-precise estimate of earnings based totally on the regression version.

Step 3 entails calculating the entire sum of squares (SST), which represents the total variant in family income. The residual sum of squares (SSE) quantifies the unexplained variation, and regression sum of squares (SSR) represents the explained variant with the aid of the regression version.

Step 4 includes checking out the statistical importance of the version using the F-statistic. The degree of importance is set at 0.052, and if the F-statistic exceeds the essential fee, the version is deemed statistically large.

Finally, the coefficient of dedication [tex]R^2[/tex] is calculated, representing the percentage of variance in own family profits defined with the aid of the mother's education. A higher [tex]R^2[/tex] shows a stronger courting between the variables. Interpreting the [tex]R^2[/tex] price allows for understanding how nicely a mom's training predicts her own family income in this context.

To know more about SSE,

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