Question

1	11	1.771
2	9	1.392
3	10	1.495
4	16	4.561
5	14	3.136
6	11	1.606
7	15	2.835
8	10	1.317
9	9	0.925
10	10	1.761
11	9	0
12	19	5.902
13	17	4.624
14	9	0.84
15	12	2.802
16	15	3.789
17	8	1.334
18	7	1.244
19	12	1.578
20	8	1.231
21	9	1.693
22	3	0
23	11	2.035
24	11	1.885
25	12	1.482
26	14	3.719
27	14	1.333
28	15	2.244
29	7	0.572
30	9	1.924
31	9	1.413
32	9	0

nStandard methodology for a single sample mean can be used to calculate a confidence interval for the slope of the least‑squares line and to test hypotheses other than H₀: ß₁= 0. In both cases, one needs to have an estimate of the slope and of its standard deviation (sometimes called standard error). Furthermore, one needs to recognize that the degrees of freedom for the standard deviation is the same as the error degrees of freedom (n ‑ 2).

Note that the EXCEL gives the standard error of estimate directly, but correctly calls it the standard deviation of the slope. Therefore, you must not divide by the square root of sample sizeas in example 16.

Use the above information to calculate a 90% confidence interval for the slope of the true regression line. For 30 degrees of freedom and a= 0.1, the critical t‑value is 1.697.

16. What is the margin of error for calculating a 90% confidence interval for the slope of the regression line (i.e. 1.697 ´the standard deviation of the slope)?

17. What is the lower 90% confidence limit for the slope?        (i.e. slope – margin of error)

18. What is the upper 90% confidence limit for the slope?

       (i.e. slope + margin of error)

                                                                                                                                                            

nUse this same information to calculate a statistic to test the null hypothesis H₀: ß₁= 0.05 against a one‑sided alternative H₁: ß₁> 0.05. Use a 1 percent significance level (for which the critical value is 2.423).

            Reminder:  t = estimated value - hypothesized value  =   slope -  0.05

                                    standard error (deviation) of estimate        st dev of slope

19. What is the value of the test statistic for testing this hypothesis?

Answer 1

16. What is the margin of error for calculating a 90% confidence interval for the slope of the regression line (i.e. 1.697 ´the standard deviation of the slope)?

0.063

17. What is the lower 90% confidence limit for the slope?        (i.e. slope – margin of error)

0.2887

18. What is the upper 90% confidence limit for the slope?

       (i.e. slope + margin of error)

0.4153

19. What is the value of the test statistic for testing this hypothesis?

8.093

	r²	0.748
	r	0.865
	Std. Error	0.700
	n	32
	k	1
	Dep. Var.	Fatals
ANOVA table
Source	SS	df	MS	F	p-value
Regression	43.5947	1	43.5947	88.98	1.75E-10
Residual	14.6983	30	0.4899
Total	58.2931	31
Regression output				confidence interval
variables	coefficients	std. error	t (df=30)	p-value	90% lower	90% upper
Intercept	-1.9425
Under 21	0.3520	0.0373	9.433	1.75E-10	0.2887	0.4153