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- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02Suppose that X ~ U (0, a) where a is a constant. Let Y = X². Calculate the %3D correlation coefficient p(X,Y).Find the marginal PDFs of X and Y.
- Q/Fit (y = ax² + (b/x)) to the following data: (x:1, 2, 3, 4), (y: -1.51, 0.99, 3.88, 7.66). *The simple correlation coefficients between temperature (X1), com yield (X2) and rainfall (X3) are r12=D0.59, r13=0.46 and r23=0.77. Calculate partial correlation coefficient r12.3 and multiple correlation coefficient R1.23Two random variables X andY are related by the expression Y = aX +b, where ta' and 'b' are any real numbers.
- Given a cross power spectrum, Sxy (w) = XY Find the cross correlation function. CS Scanned with CamScanner 8 (a + jw)³ where a > 0 is a constant.In a partially destroyed laboratory record, only the lines of regression of y on x and x on y are available as 4x – 5y +33 = 0 and 20x – 9y = 107 respectively. Calculate x, y and the coefficient of correlation between x and y.Calculate the correlation coefficient from the following results N-10, ΣX= 350 Σ Υ- 310 Σ (X-35= 162, Σ (Y- 31)" = 222, E (X- 35) (Y- 31) = 92. %3D %3D Also find the regression line of Y on X
- For the data shown to the right, determine the linear correlation coefficient using two different formulas shown below. Complete parts (a) and (b) below and compare your answers. x 1|2| 4 | 5|5 y 3 5 1 1 2 Exy - (Ex)(E) in b. Use the computing formula r= E-(Ex)*/n] E-(Ex)° /n] Find the sums required to calculate r using the computing formula. Ex-D Σ- (Type integers or decimals. Do not round.) Using the computing formula, r= (Round to three decimal places as needed.) V the value in part (b). The value in part (a) is ?Calculate correlation coefficient from the following results : N 10 ΣΧ 100 ΣΥ- 150 E(X-10}²= 180, 2(Y-15)' = 215 E(X-10(Y-15) = 60. %3DWrite a paragraph for each variable explaining what these statistics tell you about the kurtosis of the variables.
