You wish to explore the relationship between two variables, X and Y, for 17 pati

Question

You wish to explore the relationship between two variables, X and Y, for 17 patients for purposes of predicting the value of Y, given the value of X. Their corresponding values for X are: 9, 15, 10, 16, 10, 20, 11, 20, 15, 15, 8, 13, 18, 10, 8, 10, 16 and the matching (corresponding) values of Y: 45, 57, 45, 51, 65, 88, 44, 87, 89, 59, 66, 65, 56, 47, 66, 41, 56. Given this information, calculate the lower bound of the confidence interval of the slope, assuming an alpha of 0.01. Provide your answer with a level of accuracy of 1 decimal place.

Explanation / Answer

Ans:

SE = sb1 = sqrt [ (yi - i)2 / (n - 2) ] / sqrt [ (xi - x)2 ]

=SQRT(2733.97/15)/SQRT(258.47)

Sb1=0.8397

df=17-2=15

t* for 99% CI and DF=15 is 2.95

99% CI

=2.061+/-2.95*0.8397

=2.061+/-2.48

=(-0.419,4.541)

x y y'=2.061x+33.252 (y-y')^2 (x-13.176)^2 1 9 45 51.801 46.25 17.439 2 15 57 64.167 51.37 3.327 3 10 45 53.862 78.54 10.087 4 16 51 66.228 231.89 7.975 5 10 65 53.862 124.06 10.087 6 20 88 74.472 183.01 46.567 7 11 44 55.923 142.16 4.735 8 20 87 74.472 156.95 46.567 9 15 89 64.167 616.68 3.327 10 15 59 64.167 26.70 3.327 11 8 66 49.74 264.39 26.791 12 13 65 60.045 24.55 0.031 13 18 56 70.35 205.92 23.271 14 10 47 53.862 47.09 10.087 15 8 66 49.74 264.39 26.791 16 10 41 53.862 165.43 10.087 17 16 56 66.228 104.61 7.975 Mean= 13.176 60.412 2733.97 258.47 std dev= 4.019 15.476 r= 0.535 Sb1= 0.8397 slope,b= 2.061 y-intercept 33.252

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