1. An experiment was conducted to determine the relationship between x-(diameter

Question

1. An experiment was conducted to determine the relationship between x-(diameter of threaded nail) and y-(ultimate withdrawal strength. A line is fit to the data. Summary statistics are given below. n = 20, 3x = 74.66, 2-29 1.2798, Zv = 1324.095, y_ 91235.44, y= 5107.133, =3.733, = 66.20477, sx-0.8 135, sy13.7152, a= 8.9056, sxx_ 12.57402 a. Show the calculations to confirm that =17.43 and =13.07.[10 pts.] b. Calculate R2 and interpret this value. [6 pts.] Complete the test of hypothesis below. [8 pts.] 1) c. Ho: 1 = 0 versus Ha: .-0 , = 0.01 2)

Explanation / Answer

Q.1 (a)

0 =  [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

0 = [1324.095 * 291.2798 - 74.66 * 5107.133] / [20 * 291.2798 - 74.662]

0 = 4383.577/ 251.5804 = 17.424

1 =  [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

1 = [20 * 5107.133 - 74.66 * 1324.095] /  [20 * 291.2798 - 74.662]

1 = 3285.7273/ 251.5804 = 13.07

(b) R2 = [n(xy) - (x)((y)]2 / [ (n (x2 ) - (x)2) ( n (y2 ) - (y)2]

R2 = [20 * 5107.133 - 74.66 * 1324.095]2 / [20 * 291.2798 - 74.662) * (20 * 91235.44 - 1324.0952)

R2 = 3285.72732 /(251.4804 * 71481.2310)

= 0.6006

Here there are 60.06% of the variation in independent variable is explained by the variation in dependent variable.

(c) H0 : 1 =0

Ha : 1 0

Here stadard error of slope = sqrt [se2 /SSxx] = sqrt [8.90562 /12.57402] 2 = 2.5115

Test statistic

t = ^1 /se(^1) = 13.07/ 2.5115 = 5.204

so for dF = 20 - 2 = 18 and alpha = 0.05

tcritical  = 2.1000

so we shall reject the null hypothesis so we can conclude that the slope is significant.

(d) Data are normally distributed randomly.PLot b idoesn't have any problem. From plot (a) we will check the normality assumption of residuals.

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