(1) Use least-squares regression to fit a straight line to X 4 5 3 4 y 1 1 2 1.5 3 2 6 5 7 8 8 10 9 13
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- Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?For the regression model Yi = b0 + eI, derive the least squares estimator.The least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. Predict the median income of a region in which 30% of adults 25 years and older have at least a bachelor's degree.
- Question 1 Provide an algebraic proof that the least squares estimator is not consistent when Cov(x,e)=0 with the regression model y =B1+B2E(x)+e where E(e)=0 So that E(y) = B1 + B2E(x) Full explain this morning and text typing work only thanksThe least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. In a particular region, 28.3 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $37,389. Is this income higher than what you would expect? Why?A1 We want to estimate the following simple linear regression model with heteroskedas- ticity by Generalized Least Squares (GLS): yi =β0 +β1xi +ui i=1,...,n where V ar(ui|xi) = (3 + 5x2i )σ2 and σ2 is a population parameter. Explain how the GLS estimators are obtained for this specific model. Describe the underlying intuition of the GLS estimation procedure. Provide mathematical formulas
- The least-squares regression equation is y=647.8x+17,858 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7507. predict the median income of a region in which 20% of adults 25 years and older have at least a bachelor's degree. Round to the nearest dollar as needed.The least-squares regression equation is y=728.0x+14,705 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.8165. For every dollar increase in median income, the percent of adults having at least a bachelor's degree is ___%, on average. For a median income of $0, the percent of adults with a bachelor's degree is ____%.The first step of the Durbin-Watson test for the presence of autocorrelation is to estimate the model and determine Select one: a. the residuals lagged one period. b. the current period residuals and the residuals lagged one period. c. the current period residuals. d. the current period residuals, the residuals lagged one period, and the residuals lagged two periods.
- Assuming that this simple linear regression model fulfills all the classical assumptions we discussed in class, please show that the OLS estimator for the intercept of the simple linear regression model is an unbiased estimator.A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: ˆyy^=a+bxa=-1.778b=0.143 (a) Write the equation of the Least Squares Regression line of the formˆyy^= + x(b) Which is a possible value for the correlation coefficient, rr? -0.853 0.853 -1.931 1.931 (c) If a country increases its life expectancy, the happiness index will decrease increaseKolmorogov-smirnov test T-test Mann-whitney Linear Regression Are these statistical analyses could be computed in SPSS automatically?
