Question

Mid Score	Final Score
80	78
87	85
72	81
69	54
86	70
83	73
78	89
75	84
74	86
75	79
84	75
73	63
74	72
73	69
80	86
75	78
72	75
77	68
76	77
66	78
74	77
71	73
85	79
74	74
76	79
76	73
84	72
77	81
78	86
86	76
81	83
78	83
85	86
73	71
83	83
83	79
72	68
83	90
84	89
73	83
86	81
76	79
58	58
73	77
81	85
72	67
77	70
82	79
64	59
79	74
79	86
82	85
75	79
78	81
58	31
80	82
68	70
73	69

Y= 1.014 X + -1.557

R² 0.4299

e) Calculate the degrees of freedom and t-critical for a two-tailed t test for zero slope at α = .05. (Round your answers to 2 decimal places.)

Degrees of Freedom ____________ <----- Need this number

t - critical ± 2

Answer 1

e). The degrees of freedom =56

Thet-critical for a two-tailed t test for zero slope at α = .05. is 2.0032.

(The degrees of freedoms for the t-test is the same df as that of Error SS in Regression ANOVA given below:

ANOVA
	df	SS	MS	F	Significance F
Regression	1	2385.545	2385.545	42.22124	2.33E-08
Residual	56	3164.059	56.50105
Total	57	5549.603
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-1.55681	12.00042	-0.12973	0.897245	-25.5965	22.48292	-25.5965	22.48292
Mid	1.013787	0.15602	6.497788	2.33E-08	0.70124	1.326333	0.70124	1.326333