Question

A sample of n = 11 U.S. males, age 18-24 years, are measured for

height and weight. Let x denote the height in inches, and let y denote
the weight in pounds. The summary data are
Σ = 761, Σ y = 1761, Σα? = 52729, Σy? = 286273, Σαμ = 122234
From these we calculate
Sex = 81.636, Syy = 4352.9, Szy = 394.8
Find the regression line y= bo + b1
(Note: normally we would put a circumflex over the y: that is, y-"hat",
but that notation is not available in the standard math editor.

Answer 1

To find the regression line for predicting weight from height in a set of data, calculate the slope (b1) from the ratio of Sxy to Sxx and determine the y-intercept (bo) using the means of x and y. Substitute these values into the equation y = bo + b1x to obtain the final regression equation.

Step-by-step explanation:

The question revolves around finding the regression line, which is a statistical tool used to predict the value of one variable (weight) based on the value of another variable (height).

Using the given summary statistics, we calculate the slope (b1) and the y-intercept (bo) for the regression line.

The slope is computed as the ratio of Sxy to Sxx, which in this case is b1 = Sxy/Sxx = 394.8/81.636. The y-intercept is found by taking the mean of y and subtracting the product of the slope and the mean of x, which gives bo = αy/n - b1(αx/n).

Once the values are calculated, they are substituted back into the equation y = bo + b1x to form the regression equation.