Question

The dataset below contains two variables (X and Y). Please estimate the following regression model:

Y = a + bX

Based on the estimated model above, what is the predicted value of Y when X is 46?

Y	X
161	46
205	63
301	97
115	30
251	81
89	25
290	94
159	52
46	21
259	88
212	64
301	98
174	54
149	42
130	42
249	79
297	95
229	66
109	59
129	47
212	65
200	67
180	57

Question 6 options:

	144.07
	161.00
	129.05
	140.85

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Y
Independent Variable: X
Y = 4.6779286 + 3.0303126 X
Sample size: 23
R (correlation coefficient) = 0.96147942
R-sq = 0.92444267
Estimate of error standard deviation: 20.3318

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	4.6779286	12.510615	? 0	21	0.37391677	0.7122
Slope	3.0303126	0.18904974	? 0	21	16.029182	<0.0001

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	106212.19	106212.19	256.93466	<0.0001
Error	21	8681.0243	413.38211
Total	22	114893.22

Hence,

Regression equation:

= 4.678 + 3.030 x

For x = 46:

= 4.678 + 3.030*46

= 144.07

Option A is correct.