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 175 cm? use a significance level of 0.05.
president 175 188 191 183 185 192 178 177 188
opponent 173 188 169 182 177 180 180 183 175
the regression equation is ŷ = 194 + (- 0.085) 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 $\hat{y} = 194 - 0.085x$, where $x$ is the president's height (predictor variable) and $\hat{y}$ is the predicted opponent's height.

Step2: Substitute x = 188 into the equation

Substitute $x = 188$ into $\hat{y} = 194 - 0.085x$:
$$\hat{y} = 194 - 0.085 \times 188$$

Step3: Calculate the value

First, calculate $0.085 \times 188$:
$0.085 \times 188 = 16.0$ (rounded to one decimal place for intermediate step, but let's do exact calculation: $0.085\times188 = 16.0$ (since $0.085\times180 = 15.3$ and $0.085\times8 = 0.68$, so $15.3 + 0.68 = 15.98 \approx 16.0$))

Then, $\hat{y} = 194 - 15.98 = 178.02 \approx 178.0$ (rounded to one decimal place)

Answer:

178.0