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 188 cm. how close is the result to the actual opponent height of 173 cm? use a significance level of 0.05.
president 177 185 183 188 175 178 191 183 188
opponent 183 177 182 173 173 180 169 185 188
the regression equation is ŷ = 216 + (-0.205)x.
(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 188 cm is \boxed{} cm.
(round to one decimal place as needed.)

Explanation:

Step1: Identify the regression equation

The regression equation is given as $\hat{y} = 216 + (-0.205)x$, where $x$ is the height of the president (predictor variable) and $\hat{y}$ is the predicted height of the opponent.

Step2: Substitute the given value of x

We are given that the height of the president ($x$) is 188 cm. Substitute $x = 188$ into the regression equation:

$\hat{y} = 216 + (-0.205)(188)$

Step3: Calculate the value of $\hat{y}$

First, calculate $(-0.205)(188)$:

$(-0.205)(188) = -0.205 \times 188 = -38.54$

Then, add this to 216:

$\hat{y} = 216 - 38.54 = 177.46$

Step4: Round to one decimal place

Rounding 177.46 to one decimal place gives 177.5.

Answer:

177.5