(i) Find the auto-correlation of Y(t).
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A: From Part (b), the linear correlation efficient is 0.963.
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Q: From 12 observations the following results were obtained Σx =125, Σ y =437, Σxy =4997,Σ x2 =1397, Σ…
A: Givensample size(n)=12∑x=125∑y=437∑xy=4997∑x2=1397∑y2=18257
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Q: If y tends to increase linearly as x increases, the variables are _____ linearly correlated.
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- Consider a model with an interaction term between being female and being married. The dependent variable is the log of the hourly wage: log(wage) = 0.151 - 0.038 female + 0.1 married - 0.301 female* married + 0.079 educ + 0.027 exper+0.029 tenure (0.072) (0.056) (0.055) (0.007) (0.005) (0.007) n = 536, R2 = 0.461 Numbers in parantheses are standard errors of coefficients. Given the estimation result and the observation number fill in the blanks below which aim at discussing the statistical significance of variables. The test statistic of the interaction term is The critical value at 1% significance level is Then the interaction term statistically significant at 1% significance level. (Hint: to fill the blank make a choice between "is" and "is not".)A random process x(t) is applied to a network with impulse response h(t) u(t) t exp (- bt) where b>0 is a constant. The cross-correlation of x(t) with the output y(t) is known to have the same form. Rxx(t) = u(t) T exp (– bt) (a) Find the auto correlation of y(t) ? (b) What is the average power in y(t) ?T* (a) The simple correlation coefficients between temperature (X1), corn yield (X2) and 'rainfall (X3) are r12= 0.59, 13 = 0.46 and 123 = 0.77. Calculate partial correlation coefficient r123 and multiple correlation coefficient R1.23-.
- Assume that we have the usual Simple Linear Regression model given by: Y₁ = Bo + Bixi +8 Show that in this case: Where Txy R² = rzy is the correlation coefficient between x and y.Compute co-efficient of correlation from the following given results: x =10, Edx = 0. Edy = 0, E(x-K)? = 1350, Ety-7}²= 2180 and E(x-X) (y-7) =1590Consider the points in the plane: (1,2) (2,3) (3,5) (4,4) (5,7) (7,8) (i) Compute the correlation coefficient. (ii) Compute the equation for the regression line.
- Is there a linear correlation between x and y? Use α = 0.01. a.) Yes, because the correlation coefficient is not in the critical region. b.) Yes, because the correlation coefficient is in the critical region. c.) No, because the correlation coefficient is in the critical region. d.) No, because the correlation coefficient is not in the critical region. C. What is correlation coefficient when the point (2,9) is excluded? r=_________ (Round to three decimal places as needed.) Is there a linear correlation between x and y? Use α= 0.01 a.) No, because the correlation coefficient is in the critical region. b.) Yes, because the correlation coefficient is not in the critical region. c.) Yes, because the correlation coefficient is in the critical region. d.) No, because the correlation coefficient is not in the critical region.In the simple linear regression model, if there is a very strong correlation between the independent and dependent variables, then the correlation coefficient should be a) close to either -1 or +1 b) close to zero c) close to -1 d) close to +1 ( don't hand writing solution)2)If var(X) = 2, var(Y) = 5, var(Z) = 1, cov(X,Y) = 2, cov(Y,Z) = -1, and Xand Z are independent, find the correlation coefficient of U=X-2Y+Z and V=3X+Y-Z
- The value of the correlation r = (x,y) for the information would be: n = 8, Sum(x) = 609, Sum(y) = 504, Sum (x)^2 = 47995, Sum (y)^2 = 32954, and Sum (xy) = 395650 0.255 0.147 0.855 0.174A study was done to investigate the relationship between amount of protix (a new protein-vitamin•-mineral supplement) org a fortified- vitamin rice, known as FVR, and the gain in weight of children. Ten randomly chosen sections of grade one pupils were fed with FVR containing protix; different amounts X of protix were used for the 10 sections. The increase in the weight of each child was measured after a given period. The average gain Y in weight for each section with a prescribed protix level x is as follows; Section(i) Protix(X) Gain(Y) Section(i) Protix(X) Gain(Y) 1 2 3 4 5 50 60 70 80 90 91.6 96.5 95.5 101.3 104.8 6 7 8 9 10 100 110 120 130 140 105.2 107.9 107.4 109.2 109.8 Compute the prediction equation to predict the gain in the weight of a child.(d) Does a linear relation exist between the speed at which a ball is hit and the distance the ball travels? The variables speed at which the ball is hit and the distance the ball travels are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value ( ) (Round to three decimal places as needed.)