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Answer :
Final Answer:
The regression equation is [tex]\( y = 50.857 + 0.121x \)[/tex]. The best predicted weight of a supermodel who is 173 cm tall is approximately 51.1 kg.
Explanation:
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.
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