Question

Determine a 95% confidence interval for the population slope. What are the values in this confidence interval tell you? Be specific

X	Y
1870	3.38
1330	1.16
1760	1.58
1520	2.65
1300	1.98
1520	2.39
1640	2.49
1490	2.81
1300	2.95
1360	1.69
1940	3.49
1730	2.8
1790	2.95
1780	3.8
1730	2.64
1380	2.36
1580	3.1
1900	1.96
1640	3.08
1540	2.24
1350	2.59
1380	2.43
1780	1.95
1700	2.07
1610	2.34
1720	3.59
2070	3.59
1210	2.12
1720	2.48
1510	2.37
1790	2.1
2100	2.55
1690	3.01
1490	2.67
1760	1.87
1540	2.21
1810	2.37
1430	3.37
1540	1.84
1270	2.96

Answer 1

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
1870	3.38	65408.06	0.690	212.400
1330	1.16	80798.06	1.931	394.965
1760	1.58	21243.06	0.940	-141.305
1520	2.65	8883.06	0.010	-9.472
1300	1.98	98753.06	0.324	178.965
1520	2.39	8883.06	0.025	15.033
1640	2.49	663.06	0.004	-1.532
1490	2.81	15438.06	0.068	-32.367
1300	2.95	98753.063	0.160	-125.857
1360	1.69	64643.063	0.739	218.528
1940	3.49	106113.063	0.885	306.368
1730	2.8	13398.063	0.063	28.995
1790	2.95	30888.063	0.160	70.388
1780	3.8	27473.063	1.564	207.270
1730	2.64	13398.063	0.008	10.475
1380	2.36	54873.063	0.036	44.390
1580	3.1	1173.063	0.303	-18.855
1900	1.96	81653.063	0.348	-168.450
1640	3.08	663.063	0.281	13.660
1540	2.24	5513.063	0.096	22.980
1350	2.59	69828.063	0.002	-10.702
1380	2.43	54873.063	0.014	27.993
1780	1.95	27473.063	0.359	-99.367
1700	2.07	7353.063	0.230	-41.117
1610	2.34	18.063	0.044	0.890
1720	3.59	11183.063	1.083	110.033
2070	3.59	207708.063	1.083	474.208
1210	2.12	163418.063	0.184	173.625
1720	2.48	11183.063	0.005	-7.350
1510	2.37	10868.063	0.032	18.713
1790	2.1	30888.063	0.202	-79.000
2100	2.55	235953.063	0.000	0.243
1690	3.01	5738.063	0.212	34.883
1490	2.67	15438.063	0.015	-14.972
1760	1.87	21243.063	0.462	-99.037
1540	2.21	5513.063	0.115	25.208
1810	2.37	38318.063	0.032	-35.137
1430	3.37	33948.063	0.673	-151.177
1540	1.84	5513.063	0.503	52.680
1270	2.96	118508.063	0.169	-141.315

.

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	64570	101.98	1873577.500	14.1	1465.885
mean	1614.25	2.55	SSxx	SSyy	SSxy

sample size ,   n =   40          
here, x̅ = Σx / n=   1614.25   ,     ȳ = Σy/n =   2.55  
                  
SSxx =    Σ(x-x̅)² =    1873577.5000          
SSxy=   Σ(x-x̅)(y-ȳ) =   1465.9          
                  
estimated slope , ß1 = SSxy/SSxx =   1465.9   /   1873577.500   =   0.0008

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    12.906
      
std error ,Se =    √(SSE/(n-2)) =    0.58278

confidence interval for slope                  
α=   0.05              
t critical value=   t α/2 =    2.024   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    0.58278   /√   1873577.50   =   0.000
                  
margin of error ,E= t*std error =    2.024   *   0.000   =   0.001
estimated slope , ß^ =    0.0008              
                  
                  
lower confidence limit = estimated slope - margin of error =   0.0008   -   0.001   =   -0.0001
upper confidence limit=estimated slope + margin of error =   0.0008   +   0.001   =   0.0016

value of confidence interval tells that 0 is contained in it, so, slope is not significant at α=0.05