a. What is the least squares prediction equation? b. Interpret the values of B_h
ID: 3177227 • Letter: A
Question
a. What is the least squares prediction equation?
b. Interpret the values of B_hat1 and B_hat2.
c. Test for a significant linear relationship between y and X1. Find the missing t-statistic in the coefficients table.
d. Create a confidence interval for the estimate of B_hat2. Based on this interval, is the relationship between y and X2 significat?
e. Interpret R2 and Ra2.
f. Conduct the global utility test for the model.
g. In a backwards elimination procedure, which variable would be removed first?
2. Minitab was used to fit the model Ely] Bo BiX1 BrX2 to n 20 data points and the following is the output. Coef Predictor SE Coef 0.000 506.346 45 17 11.21 Constant 0.003 275.08 941.9 0.274 -429.060 X2 379.83 1.13 S 94.251 R-sq 45.9% R-Sq (adj) 39. 6% Analysis of Variance DE SS Source MIS 64165 0.005 128329 Regression 7.22 151016 8883 Residual Error 17 27 9345 TotalExplanation / Answer
a. What is the least squares prediction equation?
The prediction equation is formed using the coefficient values from the table
the equation is thus Y = 506.34 - 941.9X1 - 429.06X2
b. Interpret the values of B_hat1 and B_hat2.
Bhat1 = -941.9 , which means that for unit increase in value of X1 , Y would decrease by 941.9 units . There is an inverse relationship as we see a negative sign. We assume other variables are constant
Bhat2 = -429.06 , which means that for unit increase in value of X2 , Y would decrease by 429.06 units . There is an inverse relationship as we see a negative sign . We assume other variables are constant
c. Test for a significant linear relationship between y and X1. Find the missing t-statistic in the coefficients table.
the missing t stat is calculated as the ration of the coefficient value and the SE coefficient =-941.9/275.08
= - 3.42
As the p value of x1 isd 0.003 , which is less than 0.05 , hence we can conclude that the relationship is significant
d. Create a confidence interval for the estimate of B_hat2. Based on this interval, is the relationship between y and X2 significat?
the confidence interval can be created using the coefficients and the SE of the coefficients
bhat2 = -429.06 and corresponding SE = 379.83
so confidence interval is
bhat2 +- t(n-2)* SE , use the t tables to get the value of t (n-2) = 17 df , we see the value as 1.33 with 95% confidence
so -429.06 +- 1.33*379.83 , so the range is
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