Question

# The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2...

The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε.

 df SS MS F Significance F Regression 3 453 151 5.03 0.0030 Residual 85 2,521 30 Total 88 2,974 Coefficients Standard Error t-stat p-value Intercept 14.96 3.08 4.80 0.0000 x1 0.87 0.29 3.00 0.0035 x2 0.46 0.22 2.09 0.0400 x3 0.04 0.34 0.12 0.9066

At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant?

Multiple Choice:

• Only x1

• Only x3

• x1 and x2

• x2 and x3

Solution:

If the p-value is less than value, then it is statistically significant.

Given the value of =5%=0.05

Let us check the above condition to find the result.

 p-value Comparison Result x1 0.0035 0.0035<0.05 Significant x2 0.04 0.04<0.05 Significant x3 0.9066 0.9066>0.05 Not significant

From the above table we can see that the explanatory variables x1 and x2 is significant because its p-value is less than value.

So option 3 is the correct answer.

x1 and x2

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