a 95% confidence interval for B1, the regression slope coefficient. confidence interval for B1, the regression slope coefficient, is (Round your responses to two decin
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- Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19th century. It is from this study that the name "regression" originated. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship: Studen th = 19.6 + 0.73 × Midparh, R2 = 0.45, SER = 2.0 (7.2) (0.10) where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are heteroskedasticity robust standard errors. Interpret the estimated slope coefficient and intercept coefficient. What is the meaning of the regression R2 ? What is the prediction for the height of a child whose parents have an average height of 70.06 inches? a. b. с. d. What is the interpretation of the SER here? Is the slope coefficient statistically significantly different from zero (at the 5% significance level)? e.We have estimated the impact of gross domestic product (GDP), energy consumption (ENERGY) and population (POP) on CO2 emiisions (CO2) in Cyprus. The results are as follows, Dependent Variable: CO2 Method: Least Squares Date: 04/20/17 Time: 09.46 Sample: 1990 2013 Included observations: 24 Variable Coefficient Std. Error t-Statistic Prob. GDP ENERGY POP 2.002813 0.022114 -0.734352 0.203927 6.458672 0.011872 0.328388 0.293686 0,310097 1.862670 -2.236233 0.694371 0.7597 0.0773 0,0369 0.4954 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.825079 Mean dependentyar 0.798841 0.048515 Akaike info criterion 0.047074 Schwarz criterion 40.75460 Hannan-Quinn.criter. 31.44583 Durbin-Wats on stat 0.000000 3.625982 0.108170 -3.062883 -2.866541 -3.010793 1.410912 S.D. dependent yar a Write down the economie function for the above estimation by using the information obtained from above table| b- Write down the economic model for the above…Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19th century. It is from this study that the name "regression" originated. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship: Studenth=19.6+ 0.73x Midparh, R²=0.45, SER=2.0 (7.2) (0.10) where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are heteroskedasticity robust standard errors. (Following Galton's methodology, both variables were adjusted so that the average female height was equal to the average male height.) For the following questions except (d), type your answers in two decimal places. (a) If we test for the statistical significance of the slope coefficient, the relevant f-statistic is t = (b) Construct a 95% confidence interval for a one inch increase in the average of parental height: ( (c)…
- You have a regression: Ý 0.42 + 0.9 X₁ - 1.37X2 +0.61X3 (0.24) (0.5) (0.34) N = 50, R² = 0.67 What is the test statistic for Ho: B2 B3 B4 = 0 v.s. H₁ at least one of them is not zero. 28.71 31.13 31.8 46.7determine the regression line equation plot the line on a graph and summarize the results( reject or do not) is there enough evidence?Results of Regressions of Average Hourly Earnings on Gender and Education Binary Variables and Other Characteristics Using Data from the Current Population Survey Dependent variable: average hourly earnings (AHE). Regressor (1) (2) (3) 5.59 5.55 College (X,) 5.57 Female (X2) -2.69 -2.67 -2.67 0.30 0.30 Age (X3) 0.70 Northeast (X4) 0.61 Midwest (Xs) -0.28 South (X) Intercept 12.94 4.49 3.83 Summary Statistics SER 6.40 6.34 6.33 0.180 0.194 0.198 0.193 ok97 0.180 4100 4100 4100 Using the regression results in column (2): On average, a worker eans $ per hour for each year that he or she ages.
- A variety of summary statistics were collected for a small sample (13) of bivariate data, where the dependent variable was y and an independent variable was x. Thex variable is the number of doctorates awarded in sociology in the United States, while the y variable is the total number of space launches per year. We call this a spurious regression where the results show a relationship but the relationship is silly or utter nonsense. EX, = 7.615 ΣΥ- 583 n-13 SSE - 125.9 Estimate the least squares estimate of bo. ECY - D(X, -8) = 1.609.5 E(X, -8) = 12.466.3 E(Y - P) = 333.7 Answer:the regression R2 is 0.98.This meanY=16.8-3.9x (3.8) (1.2) The numbers 16.8 and -3.9 are the realized values for the intercept and slope (respectively) of the regression equation describing the sample, which are consistent estimators for what population parameters? The intercept and slope (respectively) of the sample determining function. The intercept and slope (respectively) of the regression equation that best fits the population. Instructions: Enter your responses rounded to three decimal places. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers: provide a 99% confidence interval for each estimator's corresponding population parameter Intercept (----------) (----------) Slope (---------) (-------------)
- The OLS estimation of the relationship between GRADE and HOURS of studying gives the following fitted equation (standard errors in parentheses): GRADEA = 38.15+0.048*HOURS (6.85) (0.01) Calculate the corresponding t statistic to test the slope coefficient for significance (Use two decimal places without rounding)In exercise 1, the following estimated regression equation based on 10 observations was presented. y^=29.1270+.5906x1+.4980x2Here SST=6724.125, SSR=6216.375, sb1=.0813, and sb2=.0567. a) Compute MSR and MSE. b) Compute F and perform the appropriate F test. Use α=.05. c) Perform a t test for the significance of β1. Use α=.05. d) Perform a t test for the significance of β2. Use α=.05.You use a dataset with 538 observations to run a simple linear regression. You find that the coefficient estimate is 3.258 and that the standard error of the coefficient estimate is 1.794. What is the lower end of the 98% confidence interval (of a two- sided test)? (you need to write a number that is rounded to the fourth digit after the decimal).