Question

1. Provide an appropriate response.

Calculate the coefficient of determination, given that the linear correlation coefficient, r, is .845. What does this tell you about the explained variation and the unexplained variation of the data about the regression line?


2. Provide an appropriate response.

Calculate the coefficient of determination, given that the linear correlation coefficient, r, is 1. What does this tell you about the explained variation and the unexplained variation of the data about the regression line?


3. Provide an appropriate response.

Find the standard error of estimate, se, for the data below, given that = -2.5x.
x -1 -2 -3 -4
y 2 6 7 10


4. Provide an appropriate response.

The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Find the standard error of estimate, se, given that y = 1.523x + 6.343
Gestation x -- 8, 2.1, 1.3, 1, 11.5, 5.3, 3.8, 24.3
Life Span y -- 30, 12, 6, 3, 25, 12, 20, 40

Answer 1

Answer: The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 0.845^2 = 0.7146. This tells us that 71.46% of the variation in the data is explained by the regression line, while 28.54% is unexplained.

The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 1^2 = 1. This tells us that 100% of the variation in the data is explained by the regression line, and 0% is unexplained.

The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = -2.5x, so we can use this equation to find the predicted values and then calculate the SSE and SEE.

The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = 1.523x + 6.343, so we can use this equation to find the predicted values and then calculate the SSE and SEE by using the given data.