Final answer:
The regression equation is calculated using the least squares method, resulting in a formula of y = mx + b, where m is the slope and b is the y-intercept. Plugging in the foot length of 272.7 mm into the equation will yield the predicted height, which can then be compared to the actual height of 1776 mm to evaluate the accuracy of the prediction.
Step-by-step explanation:
To find the regression equation for the given data of foot lengths and heights, we need to calculate the slope (m) and y-intercept (b) using the least squares regression method. Given that this is a manual calculation without the actual data analysis, we will assume that you have access to technology or statistical software that can calculate the slope and y-intercept for you based on the provided data points.
Once calculated, the regression equation will take the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept. To predict the height of a male with a foot length of 272.7 mm, plug this value into the equation as the 'x' variable. Then, compare the result to the actual height of 1776 mm to see how accurate the prediction is.
If the prediction is very close to 1776 mm, it implies the regression equation does a good job of estimating height based on foot length in the provided dataset. However, it's important to note that predictions are subject to the accuracy of the model and the variability of the data.
Example of a Regression Calculation
Suppose, after calculations, we find the slope (m) to be 3.50 and the y-intercept (b) to be 1000. Then, our regression equation would be y = 3.50x + 1000. To predict the height for a foot length of 272.7 mm:
- Substitute 272.7 into the equation for x: y = 3.50(272.7) + 1000
- Calculate the result: y ≈ 1954.45 mm
Comparing the predicted height (≈ 1954.45 mm) to the actual height (1776 mm), we can see that there's a discrepancy, implying that while the model gives an estimate, it is not always exact.