In a simple linear regression problem,suppose that = 12.48 and = 124.8.Then the percentage of variation explained must be 0.90.

Question

In a simple linear regression problem,suppose that  = 12.48 and  = 124.8.Then the percentage of variation explained  must be 0.90.

Quizplus · Accepted Answer

The percentage of variation explained is given by the coefficient of determination, R-squared, which is calculated as the square of the correlation coefficient, r.

Using the given data, we can calculate the correlation coefficient as:

r = cov(x,y)/(std(x)*std(y))

where cov(x,y) is the covariance between x and y, and std(x) and std(y) are the standard deviations of x and y, respectively.

Since we only have two data points, we can use the simplified formula:

r = (xy - n*mean(x)*mean(y))/sqrt((x^2 - n*mean(x)^2)*(y^2 - n*mean(y)^2))

where x and y are the two observations, n is the sample size (2 in this case), and mean(x) and mean(y) are the sample means.

Plugging in the values, we get:

r = (12.48*124.8 - 2*12.48*124.8)/(sqrt((12.48^2 - 2*12.48^2)*(124.8^2 - 2*124.8^2)))
  = 1

Therefore, R-squared is:

R^2 = r^2 = 1^2 = 1

This means that 100% of the variation in y (11eaaa34_f721_0937_86f9_e71d059b6dbe_TB2053_11) is explained by the linear relationship with x (11eaaa34_f720_e226_86f9_8bf77069407a_TB2053_11). Therefore, the percentage of variation explained for any other value of y, such as 11eaaa34_f721_0938_86f9_0b8e940ae466_TB2053_11, is also 100%.

Hence, the statement that the percentage of variation explained for 11eaaa34_f721_0938_86f9_0b8e940ae466_TB2053_11 is 0.90 is false.

In a Simple Linear Regression Problem,suppose That = 12