Question

QUESTION 7 Compute the least squares regression line for the given data set. Based on the data, the following are computed: 2x=33, y=63.2, 2x2 = 199, 2y =683.72, and xy = 365. x 3 8.5 4 8.4 5 10 6 113 7 11.9 8 13.1 = 0.9400x + 8.5 - 0.9943x+ 5.0648 = 0.9400x + 5.0648 D - 5.0648x +0.9943 QUESTION 8 The summary statistics for a certain set of points are: n= 18, = 8,078. Yo -57% = 7.614, and b = 1.291. Assume the conditions of the lineur model hold. Test the null hypothesis Ho Bi = 0 versus HoBj? 0. Use the a= 0.01 level of significance Test statistic is 0.160. Do not reject Ho Test statistic is 0.160. Reject Ho Test statistic is 0.441 Reject Ho Test statistic is 0.441. Do not reject Ho

Answer 1

Question 7:
х Y 3 8.5 4 8.4 5 10 6 11.3 7 11.9 8 13.1 The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used: Х Y X*Y X2 Y2 3 8.5 25.5 9 72.25 4 8.4 33.6 16 70.56 5 10 50 25 100 6 11.3 67.8 36 127.69 7 11.9 83.3 49 141.61 8 13.1 104.8 64 171.61 Sum = 33 63.2 365 199 683.72 Based on the above table, the following is calculated:


33 X - X = 5.5 n 6 i=1 η 1 Y Y; 63.2 6 10.533333333333 n 1=1 2 η SSxx = Σx? ΣΧ; = 199 – 332 /6 = 17.5 n i=1 2 SSYy = ΣΥ? = 683.72 – 63.22 / 6 = 18.013333333333 Σ' : (Σ») Στη (Σκ) (Σ) SSXY = ΣΧΥ; = 365 – 33 x 63.2/6 = 17.4 Therefore, based on the above calculations, the regression coefficients (the slope m, and the y- intercept n) are obtained as follows: m = SSXY SSxx 17.4 17.5 0.9943 η =Y – Χ. m = 10.533333333333 – 5.5 x 0.9943 = 5.0648 Therefore, we find that the regression equation is: Y = 5.0648 + 0.9943X

Hence the 4th option is the correct asnwer.

Question 8:

Test statistic = b₁ /s.e = 1.291/ 8.078 = 0.1598 ~ 0.160
Degree of freedom = n-2 = 18-2 =16
p-value = P(t₁₆ > 0.160) = 0.526 > 0.01
Hence we DO NOT reject H₀