Question

Heights (in centimetres) 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} & 174 & 176 & 178 & 178 & 176 &
174 & 176
{Weight} & 54 & 54 & 57 & 58 & 55 & 55
& 56
The regression equation is {y} =________ +__________ x . The
best predicted weight of a supermodel who is 173 cm tall is
_______

Answer 1

The regression equation is
`\( y = 50.857 + 0.121x \)`. The best predicted weight of a supermodel who is 173 cm tall is approximately 51.1 kg.

Step-by-step explanation:

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

The formula for
`\( b_1 \)`(slope) is given by:

`\[ b_1 = (N(\sum xy) - (\sum x)(\sum y))/(N(\sum x^2) - (\sum x)^2) \]`

And for
`\( b_0 \)` (y-intercept):

`\[ b_0 = (\sum y - b_1(\sum x))/(N) \]`

After calculating these values using the provided data, we obtain the regression equation
`\( y = 50.857 + 0.121x \).` 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
`\( x = 173 \)` 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.