In: Statistics and Probability
When estimating a multiple linear regression model based on 30 observations, the following results were obtained. [You may find it useful to reference the t table.]
Coefficients | Standard Error | t Stat | p-value | |
Intercept | 153.08 | 122.34 | 1.251 | 0.222 |
x1 | 12.64 | 2.95 | 4.285 | 0.000 |
x2 | 2.01 | 2.46 | 0.817 | 0.421 |
a-1. Choose the hypotheses to determine whether
x1 and y are linearly
related.
H0: β0 ≤ 0; HA: β0 > 0
H0: β1 ≤ 0; HA: β1 > 0
H0: β0 = 0; HA: β0 ≠ 0
H0: β1 = 0; HA: β1 ≠ 0
a-2. At the 5% significance level, when
determining whether x1 and y are
linearly related, the decision is to:
b-1. What is the 95% confidence interval for
β2? (Negative values should be
indicated by a minus sign. Round
"tα/2,df"
value to 3 decimal places, and final answers to 2 decimal
places.)
b-2. Using this confidence interval, is
x2 significant in explaining
y?
No, since the interval does not contain zero.
No, since the interval contains zero.
Yes, since the interval does not contain zero.
Yes, since the interval contains zero.
c-1. At the 5% significance level, choose the
hypotheses to determine if β1 is less than
20.
H0: β1 ≤ 20; HA: β1 > 20
H0: β1 ≥ 20; HA: β1 < 20
H0: β1 = 20; HA: β1 ≠ 20
c-2. Calculate the value of the test statistic.
(Negative value should be indicated by a minus sign. Round
your answer to 3 decimal places.)
c-3. At the 5% significance level, can you
conclude that β1 is less than 20?
Yes, since the null hypothesis is rejected.
Yes, since the null hypothesis is not rejected.
No, since the null hypothesis is not rejected.
No, since the null hypothesis is rejected.