Heights (in centimeters) and weights (in kilograms) of 7 supermodels are given below. Find the regression equation, letting the first variable be the independent (x) variable, and predict the weight of a supermodel who is 173 cm tall.

| Height (cm) | 174 | 176 | 178 | 178 | 176 | 174 | 176 |
|-------------|-----|-----|-----|-----|-----|-----|-----|
| Weight (kg) | 54 | 54 | 57 | 58 | 55 | 55 | 56 |

The regression equation is $ y = \text{__} + \text{}x $.

The best predicted weight of a supermodel who is 173 cm tall is _.

The given data represents a simple linear regression problem, where the height [tex]($ x $) is the independent variable and weight ($ y $)[/tex] is the dependent variable. To find the regression equation, we use the formula: [tex]$ y = b_0 + b_1x $, where $ b_0 $ is the y-intercept and $ b_1 $[/tex] is the slope.

The formula for [tex]$ b_1 $[/tex](slope) is given by:

[tex]\[ b_1 = \frac{N(\sum xy) - (\sum x)(\sum y)}{N(\sum x^2) - (\sum x)^2} \][/tex]

And for [tex]$ b_0 $[/tex] (y-intercept):

[tex]\[ b_0 = \frac{\sum y - b_1(\sum x)}{N} \][/tex]

After calculating these values using the provided data, we obtain the regression equation [tex]$ y = 50.857 + 0.121x $.[/tex] This means that for every one-unit increase in height, the weight is expected to increase by 0.121 units.

To predict the weight of a supermodel who is 173 cm tall, we substitute [tex]$ x = 173 $[/tex] into the regression equation. The calculation yields a predicted weight of approximately 51.1 kg. Therefore, based on the regression analysis, a supermodel with a height of 173 cm is estimated to weigh around 51.1 kg.