At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (with

Question

2 months ago

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At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (with

in a range). Thinking about how the person could have predicted your weight fairly accurately (despite the fact that she did not know about your "heavy bones"), you think about how this could have been accomplished. You remember that medical charts for children contain 5%, 25%, 50%, 75% and 95% lines for a weight/height relationship and decide to conduct an experiment with 110 of your peers. You collect the data and calculate the following sums: where the height is measured in inches and weight in pounds.
(a) Calculate the slope and intercept of the regression.
(b) Find the regression R2.

Mathematics

1 answer:

Leona [12.6K] · Answer 1 · 2026-03-06T15:36:18+03:00

Answer:

a) Slope: $\hat \beta_1 =\frac{7625.9}{1248.9}=6.106$

Intercept: $\hat \beta_o = 157.955 -6.106 (69.686)=-267.548$

b) $r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657$

Additionally, the coefficient of determination is $r^2 = 0.657^2 =0.432$

Step-by-step explanation:

Definitions and data provided

The correlation coefficient is a measure that quantifies the strength of the relationship between two variable movements, denoted as r and ranging between -1 and 1.

The sum of squares refers to the total of the squared deviations, where deviation is defined as the difference between each value and the grand mean.

When performing multiple regression, the aim is to analyze the relationship between multiple independent variables and one dependent variable.

n=110, $\sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9, sum y^2_i=\sum(y-\bar y)^2 =94228.8$