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Suppose you used Minitab to fit the model y=0+1x1+2x2+

to n = 15 data points and obtained the printout shown below.

  1. What is the least squares prediction equation?
  2. Find R2 and interpret its value.
  3. Is there sufficient evidence to indicate that the model is useful for predicting y? Conduct an F-test using 伪 = .05.
  4. Test the null hypothesis H0: 尾1 = 0 against the alternative hypothesis Ha: 尾1 鈮 0. Test using 伪 = .05. Draw the appropriate conclusions.
  5. Find the standard deviation of the regression model and interpret it.

Short Answer

Expert verified
  1. From the minitab printout, the prediction equation can be written as y=90.10-1.836x1+0.285x2+.
  2. Value of R2 is 0.916 meaning that approximately 92% of the variation in the regression is explained by the model. Higher the value of R2, better fit the model is for the data. Since 91.6% is a very high number, it can be concluded that the model is a good fit for the data.
  3. At 95% confidence interval, it can be concluded that120.
  4. At 95% confidence interval, it can be concluded that1=0
  5. s2=104.9230.

Step by step solution

01

Least square prediction equation

From the minitab printout, the prediction equation can be written as y=90.10-1.836x1+0.285x2+.

02

R2 interpretation

Value of R2 is 0.916 meaning that approximately 92% of the variation in the regression is explained by the model. Higher the value of R2, better fit the model is for the data. Since 91.6% is a very high number, it can be concluded that the model is a good fit for the data.

03

F-test

H0:1=2=0

Ha: At least one of the parameters 1or 2is non zero

Here, F test statistic =SSEn-(k+1)=136415-3=113.667

Value of F0.05,15,15 is 2.475

H0isrejectedifFstatistic>F0.05,15,15For=0.05,sinceF>F0.05,15,15

Sufficient evidence to reject H0 at 95% confidence interval.

Therefore, 1=2=0.

04

Significance of β1

H0:1=0Ha:10

Here, t-test statistic =1s1=-1.8360.367=-5.002

Value of t0.025,14 is 2.145

H0isrejectediftstatistic>t0.05,24,24.For=0.05,sincet<t0.05,31NotsufficientevidencetorejectH0at95%confidenceinterval.Therefore,1=0

05

Standard deviation

The standard deviation of the regression model can be calculated asSSEn-2.

Here,SSE=1364,s2=136413=104.9230.

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