Quantitative Analysis

Question 1

What is the T value of the correlation coefficient?

Answer 1

t_r = r * (sr(n-2)) / sr(1-r²)

correlation coefficient times the square root of n minus 2 divided by the square root of 1 minues the squared correlation coefficient

Question 2

What is the Standard Error of the Estimate (SEE)?

Answer 2

SEE = sq(MSR)

the square root of the mean error sum of squares

Question 3

What is the sample variance of the forecast?

Answer 3

S_f² = SEE² * ( 1 + 1/n + ((X - Xave)² / ((n-1)*S_x²)))

Question 4

What is the t-value for the slope parameter of a simple linear regression?

Answer 4

t_b1 = (b₁ - H₁) / S_b1 where H₁ = 0 for tests of statistical significance

Question 5

What is the equation for the coefficient of determination (R²)?

Answer 5

= RSS/SST

= Regression Sum of Squares divided by the Total Sum of Squares

or

= (r_x,y)² for simple linear regressions

Question 6

What is the relationship of R² and SEE to goodness of fit?

Answer 6

high R² and low SEE indicate a better fit of the regression line.

Question 7

What is the rejection rule for a two-tailed T-test?

Answer 7

reject H₀ if |t| > t_c

Question 8

What is the rejection rule for a confidence interval?

Answer 8

reject H₀ if t lies outside of the inteval

Question 9

What is the correlation coefficient?

Answer 9

r = Covariance ÷ Sx*Sy

Question 10

What is the Mean Regression Sum of Squares (MSR)?

Answer 10

MSR = RSS / k

k = number of variables