wn and yields Y^ = 5.4 + 3.2X, R2 =0.26, SER=6.2      (3.1)       (1.5)

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5. Suppose that (Yi,Xi) satisfies the least squares assumptions in Key Concept 4.3. A random sample of size n = 250 is drawn and yields
Y^ = 5.4 + 3.2X, R2 =0.26, SER=6.2

     (3.1)       (1.5)


(a)Test  H0:β1 =0    vs. H1:β1 ̸=0 at the 5% level.
(b) Construct a 95% confidence interval for β1.
(c) Suppose you learned that Yi and Xi were independent. Would you be surprised? Explain.

Expert Solution
Introduction
To determine whether the slope of the population regression line equals 0, the regression t-Test is used. 
Using the results of that test, we can determine if is good predictor of y.

The test statistic follows a t-distribution with df=n2 and can be written as:

t=β1sb

here β1 corresponds to the sample regression coefficient and sb to residual standard error 

The 100(1α)% confidence interval for β1 is given by

β1±tα2×sb

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