Question

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

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

Y = a + bX

Which of the coefficients (a and b in the equation above) are (is) statistically significant at 90% or higher confidence level?

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 5 options:

a

a and b

b

none

Homework Answers

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

From the given table of p - values,

p - value for intercept = 0.7122

p - value for slope = 0.0000

Hence,

Only b is significant.

Option C is correct.

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