The Federal Deposit Insurance Corporation (FDIC) releases data on bank failures.

Question

The Federal Deposit Insurance Corporation (FDIC) releases data on bank failures. Following are data on the number of U.S. bank failures in a given year and the total amount of bank deposits (in $ millions) involved in such failures for a given year. Use these data to develop a simple regression forecasting model that attempts to predict the failed bank assets involved in bank closings by the number of bank failures. Compute a Durbin-Watson statistic for this regression model and determine whether significant autocorrelation is present. Let = .05.

*(Round your answer to the nearest integer.)
**(Round your answer to 2 decimal places.)

The regression equation is: Failed Bank Assets =

* +

** Number of Failures

D =

**

Critical values of D: Using k = 1, n = 18, and = .05,
dL =

** and dU =

**

Since D =

** is

dU , the decision is

. There

significant autocorrelation.

Year Failures Failed Bank Assets 1 11 8,189 2 7 104 3 34 1,862 4 45 4,137 5 79 36,394 6 118 3,034 7 144 7,609 8 201 7,538 9 221 56,620 10 206 28,507 11 159 10,739 12 108 43,552 13 100 16,915 14 42 2,588 15 11 825 16 6 753 17 5 186 18 1 27

Explanation / Answer

Line of Regression Y on X i.e Y = bo + b1 X

calculation procedure for regression

mean of X = X / n = 83.2222

mean of Y = Y / n = 12754.3889

(Xi - Mean)^2 = 100155.11106

(Yi - Mean)^2 = 4932633422.28

(Xi-Mean)*(Yi-Mean) = 13689502.44438

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= 13689502.44438 / 100155.11106

= 136.68301

bo = Y / n - b1 * X / n

bo = 12754.3889 - 136.68301*83.2222 = 1379.32777

value of regression equation is, Y = bo + b1 X

Y'=1379.32777+136.68301* X

Failed Bank Assets = 1379.32777 + 136.68301 * Number of Failures

Using the excel output on regression for residual calculation,

Durbin-Watson = 2.49

dL = 1.158

dU = 1.391

If d < dL reject H0 : = 0

If d > dU do not reject H0 : = 0

If dL < d < dU test is inconclusive.

here, we are at d > dU, 2.49 > 1.391 i.e we reject Ho

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 11 8,189 5216.04617 20842776 329722.4302 7 104 5809.82377 160032339 964240.4728 34 1,862 2422.82497 118644136 536147.3449 45 4,137 1460.93657 74259391 329375.562 79 36,394 17.82697 558831213 -99811.16599 118 3,034 1209.49537 94485960 -338053.7411 144 7,609 3693.94097 26475027 -312725.4175 201 7,538 13871.61017 27210713 -614374.8086 221 56,620 18982.72217 1.924E+09 6043707.393 206 28,507 15074.38817 248144756 1934070.935 159 10,739 5742.27497 4061792.4 -152721.737 108 43,552 613.93937 948492849 763097.0483 100 16,915 281.49457 17310685 69805.90091 42 2,588 1699.26977 103355463 419080.9165 11 825 5216.04617 142310320 861566.711 6 753 5963.26817 144033336 926773.6539 5 186 6118.71257 157964400 983127.0302 1 27 6760.49017 161986428 1046473.916

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