Listed below are the heights​ (cm) of winning presidential candidates and their main opponents from several recent presidential elections. Find the regression​ equation, letting president be the predictor​ (x) variable. Find the best predicted height of an opponent given that the president had a height of 185185 cm. How close is the result to the actual opponent height of 177177 ​cm? Use a significance level of 0.05.
President
185185
192192
188188
178178
177177
183183
188188
175175
183183

Opponent
177177
180180
173173
180180
183183
182182
175175
173173
185185
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Part 1
The regression equation is ModifyingAbove y with caretyequals=196 plus left parenthesis negative 0.097 right parenthesis x196196+negative 0.097−0.097x.
​(Round the​ y-intercept to the nearest integer as needed. Round the slope to three decimal places as​ needed.)
Part 2
The best predicted height of an opponent given that the president had a height of 185185 cm is enter your response here cm.
​(Round to one decimal place as​ needed.)

### Part 1: The regression equation is:
\[
y = 196 - 0.098x
\]
(Rounding the y-intercept to the nearest integer and the slope to three decimal places.)

### Part 2: The best predicted height of an opponent, given that the president had a height of 185 cm, is:
\[
178.5 \, \text{cm}
\]
(Rounded to one decimal place.)

### How close is the prediction to the actual height?
The predicted height of 178.5 cm is approximately 1.5 cm greater than the actual height of 177 cm.

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Do you want more details or have any questions?

Here are 5 related questions to explore further:
1. What does the slope of a regression equation represent in this context?
2. How can we interpret the significance level in this regression analysis?
3. What would happen if we included more data points in the regression?
4. How do you calculate the confidence interval for a predicted value in regression?
5. How do residuals influence the accuracy of a regression model?

**Tip**: The slope in regression shows the average change in the dependent variable (opponent height) for each unit change in the independent variable (president height).

Listed below are the heights (cm) of winning presidential candidates and their main opponents from several recent presidential elections. Find the regression equation, letting president be the predictor (x) variable. Find the best predicted height of an opponent given that the president had a height of 185 cm. How close is the result to the actual opponent height of 177 cm? Use a significance level of 0.05.

Learn how to find the linear regression equation and predict the height of an opponent based on a president's height. The problem involves calculating the regression equation and using it to predict an opponent's height when the president's height is 185 cm. See how close the prediction is to the actual opponent height of 177 cm. Suitable for students in Grades 10-12.

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