Question

To whoever answers this question can you do it on paper step by step? I need a better understanding on how to solve this problem.
The following equation is the sample regression line and numbers in the parentheses are the standard errors for coefficients.
?̂ = 5.40 + 3.74 ∗ X ,? 2 = 0.26, ??? = 6.2
(3.1) (2.0)

(a) Interpret the meaning of ?0 and ?1.
(b)Construct the Z statistics to calculate the P-value to test the ?0: ?1 = 1 vs. ?1 ≠ 1 at the 5% level? Can we reject the null hypothesis?
(c) Construct a 90% confidence interval for ?1.

Answer 1

Solution:

a. The slope coefficient, is 3.74 which is interpreted as for every additional increase in X, the Y increases by 3.74.

The intercept coefficient, is 5.40, which is interpreted as when X is zero, the value of Y is 5.40.

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b. Null Hypothesis (Ho): = 1

Alternative Hypothesis (Ha): 1

Test Statistics

Z = (3.74 - 1)/2.0

Z = 1.37

Using Z-tables, the critical value at a/2 = 0.05/2 = 0.025 is 1.96

Since test statistics lies within the critical values -1.96 and 1.96, we reject Ho

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c. Using Z-tables, the critical value at a/2 = 0.10/2 = 0.05 is 1.645

90% confidence interval for is given by:-

3.74 1.645*2

3.74 3.29

0.45, 7.03