Question

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 178 cm. how close is the result to the actual opponent height of 180 cm? use a significance level of 0.05

president 185 175 178 192 191 185 177 183 183
opponent 180 173 180 180 169 177 183 185 182

the regression equation is \\(\hat{y}=169+- 0.048x\\) (round the y - intercept to the nearest integer as needed. round the slope to three decimal places as needed.)

the best - predicted height of an opponent given that the president had a height of 178 cm is \\(\square\\) cm. (round to one decimal place as needed.)

Explanation:

Step1: Identify the regression equation

The regression equation is given as $\hat{y}=189 - 0.048x$.

Step2: Substitute the given value of $x$

We are given $x = 170$. Substitute $x=170$ into the regression equation: $\hat{y}=189-0.048\times170$.

Step3: Perform the calculation

First, calculate $0.048\times170 = 8.16$. Then, $\hat{y}=189 - 8.16=180.84$.

Step4: Round the result

Rounding $180.84$ to one - decimal place, we get $\hat{y}=180.8$.

Answer:

$180.8$