Please show the process thank you! Questions 33 35 Following is a covariance mat

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Please show the process thank you! Questions 33 35 Following is a covariance matrix of 3 macroeconomic variables - GDP growth rate, inflation rate, and interest GDP growth Inflation Interest rate GDP growth Inflation Interest rate 0.3 Q33 Find the variance of GDP growth rate. (a) 1 (b) -2.1 (e) 0.3 (d) 9 (e) 4 Answer (a) 1 Q34 Find the correlation coefficient between GDP growth rate and inflation rate. (a) -0.3 (b) -0.4 (c) -0.5 (d) -0.6 (e) -0.7 Answer (d)-0.6 Q35 Find the pair of variables that have the strongest linear relationship in terms of the absolute value of the correlation coefficient. (a) (GDP growth, Inlation) (b) (GDP growth, Interest rate) (c) (Inflation, Interest rate) (d) (GDP growth, Inflation) and (GDP growth, Interest rate) are equally strongest (e) (GDP growth, Inflation) and (Inflation, Interest rate) are equally strongest Answer (a) 15

Explanation / Answer

33. option a :1

In var-covariance matrix, variance of GDP growth rate basically at the intersection of GDP growth rate at row and column which is basically 1.

34. Option D

Sd(GDP) = 1^0.5 = 1

Sd(inflation) = 9^0.5 = 3

Cov( GDP,infl) = -1.8 [simply read the matrix entry at the intersection of GDP column and inflation in the row)

Corr = Cov( GDP, Infl)/Sd(GDP)*sd(inf), where sd is standard deviation.

= -1.8/3*1 = -0.6

35. Option a

We use the same methodology described in 34 to answer 35. Below is the correlation matrix –

Corr (int rate,inflation) = 3/(3*2) = 0.5

Corr(int rate, GDP) = 0.3/(1*2) = 0.15

WE see strongest linear relationship is between GDP growth and inflation with absolute value of correlation = 0.60

GDP growth inflation interest rate GDP growth 1 inflation -0.6 1 interest rate 0.15 0.5 1

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