1. P =-1.41 + 0.0235X1 + 0. 00486x2 Predictor Coef Stdev t-ratio Constant 1.4053
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Question
1. P =-1.41 + 0.0235X1 + 0. 00486x2 Predictor Coef Stdev t-ratio Constant 1.40530 0.484800 x1 x2 0.02347 0.008666 0.001077 0.1298 Rsqe Analysis of variance Source DF SS MS Regression Error Total 1.76209 9 1.8800 a. b. Complete the missing entries in this output Compute F and test at 0.05 level of significance to see whether a significant relationship is present. c. Did the estimated regression equation provide a good fit to the data? Explain d. Use the t-test and alpha = 0.05 to test Ho: B1-0 and Ho: B2Explanation / Answer
a). Coefficient of X2 = 0.00486, This can be easily seen from the regression equation.
t-ratio of X1 = (slope of X1 - 0)/ standard deviation of the coefficient of X1 = (0.02347 - 0)/ 0.008666 = 2.7083
t-ratio of X2 = (slope of X2 - 0)/ standard deviation of the coefficient of X2 = (0.00486 - 0)/0.001077 = 4.5125
now, as df of total is 9 and we know that df of total = (n-1), where n =total number of observation, we can get 'n' from here, i.e, 9 = n-1 implies n=10.
Df of error = (total number of observations - total number of variables) = 10-3 =7, or, we can simply subtract (df of total) from (df of regression) to get (df of error).
MS for error is given by: (SS of error / df of error) = 0.11791 /7 = 0.1068
MS for total is given by: (SS of total / df of total) = 1.8800/9 = 0.2089
b). Null hypothesis: R2 = 0,
F0.05 = 4.74 (using f-table) and F= 52.44345(using our analysis) so as F>F0.05 we reject null and we have proved that R2 is different from 0 and also the relationship is significant.
c). Yes, the estimated regression equation provides a good fit as R2 is close to 1 which states that Y and X1, X2 are highly correlated, also F-test shows that it is significantly different from 0.
d). H0: B1 =0, in this case t0.05 = 2.365(using t-table at 7 df) and our t-ratio of X1= 2.7083, and as t > t0.05 , we reject H0 , similarly, for B2 ,
H0 : B2 =0 and t0.05 = 2.365, t-ratio of X2 = 4.5125 and as again t>t0.05 , we reject H0 and prove that B2 is different from 0.
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