Given are five observations for two variables, x andy. 12 35 1 The value in the

Question

Given are five observations for two variables, x andy. 12 35 1 The value in the numerator of the formula to compute the slope coefficient b is: 42 38 2 The value in the denominator of the formula to compute the slope coefficient bis 12 14 3 The value of the intercept coefficient b. is: 2.8 3.2 3.6 4.0 4 The predicted value ofy when x 8 is: 22.9 22.5 22.0 5 The prediction emor when x 8 is, -4.0 -4.5 -4.9 6 The sum of squared errors (SSE) is, 250.0 252 255.6 25 8.4 7 The standard error of estimate, se e, for the model is: 230 8.584 7.983 7.425 The sum of squares total (SST is, 261.0 273.7 449.2 9 The sum of squares regression (SSR) is 193.6 191.8 188.2 10 The fraction of variations in y explained by x is 0.4072 0.43 0.4606 4947

Explanation / Answer

Back-up Theory

Let X and Y be two variables such that Y depends on X by the model Y = + X + , where is the error term, which is assumed to be Normally distributed with mean 0 and variance 2.

Let (xi, yi) be a pair of sample observation on (X, Y), i= 1, 2, …., n

where n = sample size.

Then, Mean X = Xbar = (1/n)sum of xiover I = 1, 2, …., n; ……………….(1)

Sxx = sum of (xi – Xbar)2 over i = 1, 2, …., n ………………………………..(2)

Similarly, Mean Y = Ybar =(1/n)sum of yiover i= 1, 2, …., n;…………….(3)

Syy = sum of (yi – Ybar)2 over i = 1, 2, …., n ………………………………………………(4)

Sxy = sum of {(xi– Xbar)(yi– Ybar)} over i = 1, 2, …., n………(5)

Estimated Regression of Y on X is given by: Y = a + bX, where

b = Sxy/Sxx and a = Ybar – b.Xbar..…………………….(6)

Now, to work out solution,

n = 5; Using Excel Functions, the following are computed with the given data:

Xbar = 17.6; Ybar = 7;   Syy = 10;   Sxx= 449.2 Sxy = 44;    b = 0.0980   a = 5.276;       

Estimated Regression of Y on X is: y = 5.276 + 0.0920x.

Part (a)

Slope coefficient is b. So, numerator of slope coefficient = Sxy = 44 ANSWER

Part (b)

Slope coefficient is b. So, denominator of slope coefficient = Sxx = 449.2 ANSWER

Part (c)

Intercept coefficient is a = 5.276 ANSWER

Part (d)

Predicted value of y when x = 8 is obtained by substituting x = 8 in the Estimated Regression of Y on X: y = 5.276 + 0.0920x. So, Predicted value of y when x = 8 is

5.276 + 0.0920x8 = 6.06 ANSWER

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