Question

The following data give the number of hours 1010 students spent studying and their corresponding grades on their midterm exams.

Hours Studying	0.50.5	0.50.5	11	22	22	3.53.5	3.53.5	4.54.5	55	5.55.5
Midterm Grades	6161	6565	6565	6565	7373	7878	7878	8383	9090	9090 Table Copy Data Step 1 of 5: Calculate the sum of squared errors (SSE). Use the values b0=59.1253b0=59.1253 and b1=5.5981b1=5.5981 for the calculations. Round your answer to three decimal places. Calculate the estimated variance of errors, s2ese2. Round your answer to three decimal places. Calculate the estimated variance of slope, s2b1sb12. Round your answer to three decimal places. Construct the 90% confidence interval for the slope. Round your answers to three decimal places. (lower endpoint and upper endpoint) Construct the 80% confidence interval for the slope. Round your answers to three decimal places. (lower endpoint and upper endpoint)

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
0.5	61	5.29	190.44	31.74
0.5	65	5.29	96.04	22.54
1	65	3.24	96.04	17.64
2	65	0.64	96.04	7.84
2	73	0.64	3.24	1.44
3.5	78	0.49	10.24	2.24
3.5	78	0.49	10.24	2.24
4.5	83	2.89	67.24	13.94
5	90	4.84	231.04	33.44
5.5	90	7.29	231.04	41.04

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	28	748	31.1	1031.600	174.100
mean	2.800	74.800	SSxx	SSyy	SSxy

a)SSE=   (SSxx * SSyy - SS²xy)/SSxx =    56.976

b) estimate of variance,   Se² = SSE/(n-2) =    7.122

c) estimated varince of slope ,    Se²(ß1) = Se²/Sxx =    0.229

d) confidence interval for slope                  
α=   0.1              
t critical value=   t α/2 =    1.860   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    2.66870   /√   31.10   =   0.479
                  
margin of error ,E= t*std error =    1.860   *   0.479   =   0.890
estimated slope , ß^ =    5.5981              
                  
                  
lower confidence limit = estimated slope - margin of error =   5.5981   -   0.890   =   4.708
upper confidence limit=estimated slope + margin of error =   5.5981   +   0.890   =   6.488

e)

confidence interval for slope                  
α=   0.2              
t critical value=   t α/2 =    1.397   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    2.66870   /√   31.10   =   0.479
                  
margin of error ,E= t*std error =    1.397   *   0.479   =   0.668
estimated slope , ß^ =    5.5981              
                  
                  
lower confidence limit = estimated slope - margin of error =   5.5981   -   0.668   =   4.930
upper confidence limit=estimated slope + margin of error =   5.5981   +   0.668   =   6.267