Question

Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 15.4 20.3 14.4 19.6 20.0 Σx = 15; Σy = 89.7; Σx2 = 55; Σy2 = 1,640.77; Σxy = 277.6 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) %

Answer 1

Given: x and y variables.

n = number of pairs of (x, y) = 5

(a)

The general least squares regression equation is,

Where a - intercept and b - slope

The formulas to find the slope and intercept are

The equation of the least square line is,

(b) Scatter diagram:

Scatter diagram using excel with a least-square line is

(c) The sample correlation coefficient(r)

The formula to find the correlation coefficient is,

r = 0.479

r² - coefficient of determination = r * r = (0.479)² = 0.229

r² = 22.9%

That is 22.9% of variation in y is explained by the least-squares model.