Question

worker wages los size 1 52.0194 79 Large 2 37.4279 33 Small 3 44.6883 76 Small 4 38.2653 113 Small 5 73.4314 126 Large 6 44.2075 94 Small 7 46.0139 16 Large 8 59.7869 63 Large 9 54.5961 41 Large 10 46.8283 114 Small 11 39.9753 20 Large 12 78.1773 76 Small 13 62.8463 191 Small 14 43.6917 136 Large 15 51.1155 38 Large 16 40.8005 121 Large 17 68.3245 85 Large 18 56.1802 21 Small 19 64.239 116 Large 20 56.1115 30 Large 21 43.0836 81 Large 22 64.9279 72 Small 23 64.4067 85 Large 24 38.9084 71 Small 25 46.4535 42 Large 26 50.193 47 Small 27 61.8212 44 Small 28 37.3811 80 Large 29 43.738 29 Large 30 50.1786 149 Large 31 40.0233 110 Small 32 66.2606 63 Large 33 38.982 99 Large 34 41.4998 59 Small 35 51.4911 33 Large 36 45.6895 73 Large 37 42.7866 25 Large 38 46.0938 46 Small 39 44.327 112 Large 40 58.1332 18 Small 41 39.2811 24 Small 42 37.4001 17 Small 43 50.9489 73 Large 44 49.9768 84 Small 45 44.3607 121 Large 46 43.225 16 Small 47 44.5352 21 Large 48 55.0402 62 Large 49 41.2324 18 Small 50 51.7267 48 Large 51 65.6027 24 Large 52 67.2068 32 Large 53 41.3341 56 Large 54 50.1268 132 Small 55 48.1182 144 Small 56 48.6569 47 Large 57 79.0857 159 Small 58 48.6652 51 Large 59 48.0831 30 Small 60 53.6059 135 Large We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample of employees at a given point in time, we can look at part of the picture. How does length of service (LOS) relate to wages? The data here (data211.dat) is the LOS in months and wages for 60 women who work in Indiana banks. Wages are yearly total income divided by the number of weeks worked. We have multiplied wages by a constant for reasons of confidentiality. (a) Plot wages versus LOS. Consider the relationship and whether or not linear regression might be appropriate. (Do this on paper. Your instructor may ask you to turn in this graph.) (b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude? Wages = + LOS t = P = (c) State carefully what the slope tells you about the relationship between wages and length of service. (d) Give a 95% confidence interval for the slope. ( , )

Answer 1

Solution:-

a)

b)

Wages = 29.839 + 0.7984*LOS

t-value= 1.507

p-value = 0.1371

c) The t-test for the slope tells that there is evidence that slope of the regresison line is zero, hence the correlation coefficient is also near to 0.

d) 95% confidence inetraval of the slope is (- 0.2617, 1.86).

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