Part C: True or False (36-40) .36. In the least squares model, the explained sum

Question

Part C: True or False (36-40) .36. In the least squares model, the explained sum of squares is always smaller than the regression sum of squares. 37. The sample correlation coefficient and the sample slope will always have the same sign. 38. Given the sample regression equation y = 4-3x, we know that in the sample X and Y are inversely related. 39. Given the sample regression equation y = 5-6, we know that when x-2, Y = 17. 40. If zero is contained in the 95% confidence interval for b, we may reject Ho: b-0 at - the 0.05 level of significance. Part D: Must show all your work step by step in order to receive the full credit: Excel is not allowed.(41-57 41) A large hotel purchased 200 new color televisions several months ago: 80 of one brand and 60 of each of two other brands. Records were kept for each set as to how many service calls were required, resulting in the table that follows Sony 30 60 Number of Service Calls Total TV Brand Toshiba None One 15 18 12 30 60 41 97 62 200 10 80 Two or more Total Assume the TV sets are random samples of their brands. With 5% risk of Type I error, test for an association between TV brand and the number of service calls. Is the 2 value significant at 5% level of significant? write the conclusion for this question.

Explanation / Answer

Part (C)

36. False
since explained sum of square and regression sum of square are same

37. True

38. True
since slope = -3 which is <0

39. False
since estimated value of Y = 5-6*2 = -7

40. False

Part (D)

H0: There is no association between TV brand and number of service calls

H1: There is association between TV brand and number of service calls

Let the los be alpha = 5%

The expected frequencies are

The chisquare contribuiton values are calculated as follows

Test Statistic, X^2: 37.5453

Degrees of freedom: 4

Critical X^2: 9.48772
P-Value: 0.0000

Here P-value < alpha 0.05, and Chisquare value > chisquare critical value, so we reject H0

thus we conlcude that   there is association between TV brand and number of service calls

The Expected frequencies are sony toshiba sanyo Total None 12.3 16.4 12.3 41 one 29.1 38.8 29.1 97 two or mote 18.6 24.8 18.6 62 Total 60 80 60 200

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