Question

The following data give the number of hours 5 5 students spent studying and their corresponding grades on their midterm exams. Hours Studying   Midterm Grades
1   74
2   86
3   91
3   94
5   97

Step 1 of 5 : Calculate the sum of squared errors (SSE). Use the values b0=73.0000 b 0 = 73.0000 and b1=5.5000 b 1 = 5.5000 for the calculations. Round your answer to three decimal places.

Step 2 of 5:

Calculate the estimated variance of errors, s2ese2. Round your answer to three decimal places.

Step 3 of 5:

Calculate the estimated variance of slope, s2b1sb12. Round your answer to three decimal places.

Step 4 of 5:

Construct the 99% confidence interval for the slope. Round your answers to three decimal places.

Lower:

Upper:

Step 5 of 5:

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

Lower:

Upper:

Answer 1

step 1)

X	Y				Ŷ=73+5.5*x	residual,ei=Y-Y^	SSE = (Y-Ŷ)²
1	74				78.50	-4.500	20.25
2	86				84.00	2.000	4.000
3	91				89.50	1.500	2.250
3	94				89.50	4.500	20.250
5	97				100.50	-3.500	12.250

SSE=   Σ(Y-Ŷ)² = 59.000

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step 2)

estimate of variance,   Se² = SSE/(n-2) =    19.667

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step 3)

SSxx =    Σ(x-x̅)² =    8.8000

estimated varince of slope ,    Se²(ß1) = Se²/Sxx =    2.235

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step 4)

α=   0.01              
t critical value=   t α/2 =    5.841   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    4.43471   /√   8.80   =   1.495
                  
margin of error ,E= t*std error =    5.841   *   1.495   =   8.732
estimated slope , ß^ =    5.5000              
                  
                  
lower confidence limit = estimated slope - margin of error =   5.5000   -   8.732   =   -3.232
upper confidence limit=estimated slope + margin of error =   5.5000   +   8.732   =   14.232

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step 5)

confidence interval for slope                  
α=   0.2              
t critical value=   t α/2 =    1.638   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    4.43471   /√   8.80   =   1.495
                  
margin of error ,E= t*std error =    1.638   *   1.495   =   2.448
estimated slope , ß^ =    5.5000              
                  
                  
lower confidence limit = estimated slope - margin of error =   5.5000   -   2.448   =   3.052
upper confidence limit=estimated slope + margin of error =   5.5000   +   2.448   =   7.948