Question 1 14 marks] An investor wants to know how SP Index is affected by chang

Question

Question 1 14 marks] An investor wants to know how SP Index is affected by changes in CPI index in Australia. He collected data over 17 weeks on SP and CPI indexes and run the linear regression. The summary output from excel are reported below Regression Statistics Multiple R R Square Observations 0.965 0.93 Coefficients Standard Error t Stat 8.71 Intercept CPI 58.99 0.48 6.8 Use the above output for answering the following questions i) Calculate the missing values from the summary output: A and B(2 mark) ii) Interpret the slope of the regression line iii) Write down the estimated linear regression line iv) What is the value of coefficient of determination? Interpret this value. (2 mark) v) What is the value of the coefficient of correlation? Interpret this value. (2 mark) (2 mark) (1.5 mark) Test the hypothesis that the estimated slope coefficient is less than zero (at a 5% (3 marks) (1.5mark) level) vii) Predict SP Index if the CPI index is 180

Explanation / Answer

(i) Here A/58.99 = -8.71

A = 58.99 * (-8.71) = -513.8029

B = 6.8/0.48 = 14.167

(ii) The slope here is 6.8 that means if there is a change of 1 unit in CPI index, there will be a change of 6.8 units in SP index.

(iii) Linear regression Line

y^ = A + 6.8 * x

where y^ = SP index and x = CPI index

y^ = -513.8029 + 6.8x

(iv) Coefficient of determination = 0.93

Here we can see that 93% of variability in SP index that can be predicted from the CPI Index.

(v) Coefficient of correlation r = sqrt(0.93) = 0.9644

It is a measure of the strength and direction of the linear relationship so as the value of r is 0.9644.

(vi) H0 : 1 < 0

Ha : 1 > 0

Test statistic

t = 6.8/0.48 = 14.167

tcr = 2.306

so we shall reject the null hypothesis and can conclude that null hypothesis is correct.

(vii) if CPI index = 180

SP Index = -513.8029 + 6.8x = -513.8029+ 6.8 * 180 = 710 .20

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