Question

4) A study was done on yearly musicals watched (M) and personal awesomeness (A) Observation Awesomeness (A) Musicals Watched (M) 2 6 2 3 10 5 5 a) Calculate sample mean of A and M b) Calculate variance and standard deviation of A and M. c) Calculate covariance and correlation between A and M. Interpret. d) Use OLS to estimate the following equation, including predicted values, residuals and R2. (Remember to always report OLS in the manner seen in class.) + S

Answer 1

a) Mean (A)- (8+6+10)/3 -8 Mean (M) (5+2+5)/3-4 b) Variance (A)-[(8-8)2 +(6-8)2 + (10-8)-1/3-2.67 Standard deviation (A) sqrt(2.67) 1.63 Variance (M)-[(5-4)2 + (2-4)24 (54)213-2 Standard deviation (Mrt(2) 1.41 c) Covariance: -covar(8,6,10, 5,2,5)-2 Correlation: correl(8,6,10, 5,2,5)-0.866 d) Regression results in Excel SUMMARY OUTPUT Regression Statistics Multiple R Square Adjusted R Square Standard Error Observations 0.866025404 0.75 0.5 .414213562 Coefficients Standard Error t Stat P-value 4 2.449489743 1.632993162 0.349801712 1 0.577350269 1.732050808 0.333333333 Intercept

Equation: A-41M R-squared 0.75 or 75% RESIDUAL OUTPUT Observation Predicted A Residuals -1 0 6