In a simple linear regression based on 27 observations, it is found that b1 = .4
ID: 3269274 • Letter: I
Question
In a simple linear regression based on 27 observations, it is found that b1 = .46 and se(bj) = .26. Consider the hypotheses (Use Table 2): H0: 1 0 and HA: 1 > 0
a. At the 5% significance level, find the critical value(s). (Round your answer to 3 decimal places.) Critical value
b. Calculate the value of the appropriate test statistic. (Round your answer to 2 decimal places.) Test statistic
c. At the 5% significance level, what is the conclusion to the hypothesis test? Does the explanatory variable have a positive effect on y?
Reject H0Picture the explanatory variable has a positive effect on y.
Do not reject H0Picture the explanatory variable does not have a positive effect on y.
Reject H0Picture the explanatory variable does not have a positive effect on y.
Do not reject H0Picture the explanatory variable has a positive effect on y.
Explanation / Answer
a)
df= n-1 = 27-1 = 26
for 5% significance level, critical value for right-tailed test is 1.706
b) TS = b1/se(b1) = 0.46/0.26 = 1.769230
c) since TS > t-critical
we reject the null and conclude that the explanatory variable have a significant positive effect on y.
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