Listed below is a company's sales inYear 1 through Year 12 along with the national income of the country, where thebusiness is set up.
Year
National Income (in millions of dollars) x
Company's sales (in thousands of dollars) y
Year 1
305
470
Year 2
316
485
Year 3
358
499
Year 4
350
515
Year 5
375
532
Year 6
392
532
Year 7
400
556
Year 8
398
576
Year 9
430
583
Year 10
456
587
Year 11
578
601
Year 12
498
605
Test whether each of the regression parameters?0 and?1 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters?
What will be an ideal response?
The Excel plot of the residuals and market capitalization follows.
Because we are working with only 12 observations, assessing the conditions necessary for inference to be valid in regression is extremely difficult. However, this scatter chart does not provide strong evidence of a violation of the conditions, so we will proceed with our inference.
Excel output:
The p value associated with the estimated regression parameter b1 is 8.9E-05, which is 0.000089, or approximately equal to 0. Because this p value is less than the 0.05 level of significance, we reject the hypothesis that?1= 0. Hence, we conclude that there is a relationship between national income and the company's sales, and, on average, a $1 million increase in national income corresponds to an increase of $534.02 in the company's sales. The company's sales are expected to increase as national income increases, so this result is consistent with what is expected.
The p value associated with the estimated regression parameter b0 is 2.7E-06 which is 0.0000027, or approximately equal to 0. Because this p value is less than the 0.05 level of significance, we reject thehypothesisthat?0= 0. The estimated regression parameter b0 suggests that when national income is zero, the company's sales are $328,981, which is not a realistic estimate.
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