Question

The data in the table is the number of absences for 77 students and their corresponding grade.

Number of Absences	33	55	66	66	66	77	88
Grade	3.93.9	3.83.8	2.92.9	2.72.7	2.42.4	2.32.3	1.91.9

Step 1 of 5 : Calculate the sum of squared errors (SSE). Use the values b0=5.4276b0=5.4276 and b1=−0.4413b1=−0.4413 for the calculations. Round your answer to three decimal places.

step2: Calculate the estimated variance of errors, se2. Round your answer to three decimal places.

step3 : Calculate the estimated variance of slope, sb12. Round your answer to three decimal places.

step 4: Construct the 90%confidence interval for the slope. Round your answers to three decimal places.

step 5: Construct the 80% confidence interval for the slope. Round your answers to three decimal places.

Answer 1

step 1)

x	y	(x-x̅)²			Ŷ=5.4276-0.4413   *x	residual,ei=y-yhat	(Y-Ŷ)²
3	3.9	8.16			4.104	-0.204	0.04
5	3.8	0.73			3.221	0.579	0.34
6	2.9	0.02			2.780	0.120	0.01
6	2.7	0.02			2.780	-0.080	0.01
6	2.4	0.02			2.780	-0.380	0.14
7	2.3	1.31			2.338	-0.038	0.00
8	1.9	4.59			1.897	0.003	0.000

SSE=   Σ(Y-Ŷ)² = 0.543

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2)

estimate of variance,   Se² = SSE/(n-2) =    0.109
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3)

estimated varince of slope ,    Se²(ß1) = Se²/Sxx = =0.109/14.857 = 0.0073

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4)

confidence interval for slope                  
α=   0.1              
t critical value=   t α/2 =    2.015   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    0.32960   /√   14.86   =   0.086
                  
margin of error ,E= t*std error =    2.015   *   0.086   =   0.172
estimated slope , ß^ =    -0.4413              
                  
                  
lower confidence limit = estimated slope - margin of error =   -0.4413   -   0.172   =   -0.614
upper confidence limit=estimated slope + margin of error =   -0.4413   +   0.172   =   -0.269
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5)

confidence interval for slope                  
α=   0.2              
t critical value=   t α/2 =    1.476   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    0.32960   /√   14.86   =   0.086
                  
margin of error ,E= t*std error =    1.476   *   0.086   =   0.126
estimated slope , ß^ =    -0.4413              
                  
                  
lower confidence limit = estimated slope - margin of error =   -0.4413   -   0.126   =   -0.568
upper confidence limit=estimated slope + margin of error =   -0.4413   +   0.126   =   -0.315