9-16. Given that the regression equations of Y on X and of X on Y are respectively Y = X and 4X - Y = 3, and that the second moment of X about the origin is 2, find (a) the correlation coefficient between X and Y and (b) the standard deviation of Y.
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- The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.Consider the following regression equation specied for 2-period panel data: where i = 1; 2; :::N and t = 1; 2. If you expect that β_1 is positive, but the correlation between Δx_i and Δu_i is negative, thenwhat is the bias in the OLS estimator of β_1 in the first-differenced equation?The birth lengths in cm (x) and birth weights in kg (y) of a sample of 50 newborn female babies are compared, yielding a correlation coefficient of r=0.578 and a linear regression equation of ŷ =−8.89+0.243x The babies all had lengths between 46.5 and 53.0 cm, and weights between 2.50 and 4.05 kg. Based on this, predict the birth weight of a newborn female baby with a birth length of 48.5 cm.
- Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. Using the 68-95-99.7 rule, between what two values would approximately 95% of the observed responses, y, fall when x = 7?The following estimated regression equation based on 10 observations was presented. ŷ = 29.1670 + 0.5902x1 + 0.4960x2 Here, SST = 6,734.125, SSR = 6,212.375, sb1 = 0.0816, and sb2 = 0.0569. (a) Compute MSR and MSE. (Round your answers to three decimal places.) MSR=?? MSE=?? (b) Compute F and perform the appropriate F test. Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 = ?2 = 0 Ha: One or more of the parameters is not equal to zero. H0: ?1 > ?2 Ha: ?1 ≤ ?2 H0: ?1 ≠ 0 and ?2 ≠ 0 Ha: One or more of the parameters is equal to zero. H0: ?1 < ?2 Ha: ?1 ≥ ?2 H0: ?1 ≠ 0 and ?2 = 0 Ha: ?1 = 0 and ?2 ≠ 0 Find the value of the test statistic. (Round your answer to two decimal places.) F = ?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is sufficient evidence to conclude that the overall model is significant. -Do not reject H0.…The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is _____.
- The following estimated regression equation based on 10 observations was presented. ŷ = 27.1870 + 0.5709x1 + 0.4920x2 Here, SST = 6,734.125, SSR = 6,213.375, sb1 = 0.0815, and sb2 = 0.0561 a. Compute MSR and MSE. (Round your answers to three decimal places.) b. Compute F and perform the appropriate F test and find p vaule. Use ? = 0.05. State the null and alternative hypotheses. state your conclusion c. Perform a t test for the significance of b1. Use a = 0.05. d. Perform a t test for the significance of b2. Use a = 0.05.X” denote the number of children ever born to a woman, and let “Y” denote years ofeducation for the woman. A simple model relating fertility to years of education is X = β0 + β1Y + u where u is the unobserved error. (i) What kind of factors are contained in u? Are these likely to be correlated with level of education?Consider the following simple linear regression model: y = β0 + β1x + u. Using a sample of n observations on x and y, you estimate the model by OLS and obtain the estimates βˆ 0, βˆ 1, and the R-squared of the regression, R2 . Then you scale this sample by a factor of 100, obtain a new sample {xi/100; yi/100} for i = 1, . . . , n, re-estimate the model by OLS, and denote the new coefficient estimates by β˜ 0, β˜ 1, and the new R-squared of the regression by R˜2 . a) Give the expression of β˜ 1 in terms of βˆ 1, and justify your answer.
- A set of n = 4 pairs of X and Y values has a Pearson correlation of r = 0.60 and SSY = 200. The standard error of estimate for the regression equation is _______. a. 8 points b. 10 points c. 6 points d. 4 points7. in a regression model involving 44 observations, the following estimated regression equation was obtained. Y =29+18 X1 +43 X2 +87 X3 For this model SSR = 600 and SSE = 400 . The critical value of F for testing the significance of the above model at 5% level is A. 2.61 B. 0.67 C. 2.84 D. None E. 8.59There is a relation between the following variables as y = 1 / (a * x ^ b) (x ^ b means x over b) a) Calculate the correlation coefficient and interpret the degree of the relationship? b) Estimate the y-value for x = 4.3 and the x-value for y = 0.90 by obtaining the regression equation