(f) Plot 95% confidence limits for the mean response on the graph around the regression line.
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Solve Part F. Please and Thank You.
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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 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?A regression on the original regressors, ?̂t2 and a constant term yields the following statistics: R2 = 0.296041 F = 1.177507 coeff of ?̂t2 has a t-statistic of 2.876 With this information, which test can you implement to deal with the problem omitted variables and why? Implement the test as stated in b(i) and interpret the results. What is (are) the consequence(s) of the problem alluded to above on the estimators?
- 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?Use the following linear regression equation to answer the questions. (d) x1 = 1.0 + 3.9x2 – 8.4x3 + 2.4x4 Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?Suppose x2 increased by 2 units. What would be the expected change in x1?Suppose x2 decreased by 4 units. What would be the expected change in x1?(e) Suppose that n = 8 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.468. Construct a 90% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 5%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t t critical ±Which of the following expressions is the correct way to express an interpretation for an OLS regression coefficient of -0.9? - This question is based on Data Analysis A. For every one unit increase in X there is - on average - a 0.9 unit decrease in Y. B. For every one unit increase in Y there is - on average - a 0.9 unit decrease in X. C. For every one unit increase in Y there is - on average - a 0.9 unit increase in X. D. For every one unit increase in X there is - on average - a 0.9 unit increase in Y.
- In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 16.7 + 3.5x1 − 2.3x2 + 7.9x3 + 2.9x4 (a)Interpret b1 in this estimated regression equation. -b1 = 7.9 is an estimate of the change in y corresponding to a 1 unit change in x3 when x1, x2, and x4 are held constant. -b1 = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x4 when x1, x2, and x3 are held constant. -b1 = 3.5 is an estimate of the change in y corresponding to a 1 unit change in x1 when x2, x3, and x4 are held constant. -b1 = 3.5 is an estimate of the change in y corresponding to a 1 unit change in x2 when x1, x3, and x4 are held constant. -b1 = −2.3 is an estimate of the change in y corresponding to a 1 unit change in x1 when x2, x3, and x4 are held constant.Interpret b2 in this estimated regression equation. -b2 = −2.3 is an estimate of the change in y corresponding to a 1 unit change in x1 when x2, x3, and x4 are held…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?The following estimated regression equation based on 10 observations was presented. ŷ = 29.1260 + 0.5306x1 + 0.4680x2 The values of SST and SSR are 6,728.125 and 6,215.375, respectively. (a) Find SSE. SSE = (b) Compute R2. (Round your answer to three decimal places.) R2 = (c) Compute Ra2. (Round your answer to three decimal places.) Ra2 = (d) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.The estimated regression equation did not provide a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation provided a good fit as a large proportion of the variability in y has been explained by the estimated regression equation.
- Consider the following four quantities for a regression coefficient: the estimate of the coefficient, the standard error of the coefficient, the t-value of the coefficient, and the p-value of the coefficient. Which of the following is true? a. If the standard error increases and the estimate itself doesn't change, the magnitude of the t-value will decrease and the p-value will decrease. b. If the standard error decreases and the estimate itself doesn't change, the magnitude of the t-value will increase and the p-value will decrease. c. If the standard error decreases and the estimate itself doesn't change, the magnitude of the t-value will increase and the p-value will increase. d. If the standard error increases and the estimate itself doesn't change, the magnitude of the t-value will increase and the p-value will decrease.1) Find the regression equation and r value Drop Height, y (m) Square of Mean Fall time, t^2 (s^2) 0.100 0.0188 0.300 0.0576 0.500 0.0980 1.000 0.198 1.500 0.305 2.500 0.508A scientist is interested in whether there is a linear relationship between the amount of mercury in a lake and the surface area of the lake. The scientist collected data on 22 lakes of a similar type selected at random and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim. H0:β=0 Ha:β≠0 The test yielded a t-value of 2.086 with a corresponding p-value of 0.05. Which of the following is the correct interpretation of the p-value? A. If there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic as extreme as 2.086 or more extreme is 0.05 B. If there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 is 0.05. C. If there is not a linear relationship between the amount of mercury in a lake and the surface area of the lake, the…
