Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. The table shows the shoe size and heights​ (in.) for 6 men.
font size decreased by 1 font size increased by 1 Shoe size comma x
6.5
7.0
8.0
9.0
12.0
13.0

​Height, y
65.0
66.0
69.0
72.0
72.0
73.0
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Part 1
Find the regression equation.
ModifyingAbove y with caretequalsnothing x plus left parenthesis nothing right parenthesis

​(Round to three decimal places as​ needed.)

Here is the scatter plot with the regression line based on the given data. 

The regression equation is:
\[ y = 57.411 + 1.308x \]

This equation indicates that for each additional unit increase in shoe size, the height increases by approximately 1.308 inches, starting from a base height of 57.411 inches when the shoe size is zero.

Do you have any questions or would you like more details on any part of the solution?

Here are some related questions to expand your understanding:

1. How do we interpret the slope in the context of this problem?
2. What does the y-intercept represent in this regression equation?
3. How can we use the regression equation to predict the height for a shoe size of 10?
4. What are residuals, and how can we calculate them for this data?
5. How do we measure the goodness of fit for the regression line?
6. What is the coefficient of determination (\( R^2 \)), and how is it calculated?
7. How would the regression equation change if an outlier was added to the data set?
8. What assumptions are made when performing linear regression analysis?

**Tip:** When plotting regression lines, always check the residuals to ensure there is no pattern, indicating a good fit for the linear model.

Learn how to construct a scatter plot and find the regression equation for given data on shoe sizes and heights. The regression equation derived is y = 57.411 + 1.308x, indicating the relationship between shoe size and height. Suitable for high school students studying linear regression.

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