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In: Statistics and Probability

When estimating a multiple linear regression model based on 30 observations, the following results were obtained....

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:

  • Reject H0x1 and y are linearly related.
  • Reject H0x1 and y are not linearly related.
  • Do not reject H0we cannot conclude x1 and y are linearly related.

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.

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