Given a simple linear regression model, y=+B+, which following expressions are OLS estimators for ? i Σ(x₂-x)y; i=1 Σ(x,-1) ² i=1 i Ο Σ-16-06-5) Σ₁(x, -x) ² i=1 xy 2² X i=1
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- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.Given the following five points: (-2,0),(-1,0),(0,1)(1,1) and (2,3). if the regression equation is Y' = 2-0.4X, What is the value of Y' when X =-3?
- 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.also compute the regression equation in which you predict Y using X as the predictor variableIn the equation, Y’ = b0 + bxX, b0 represents the: Group of answer choices correlation between X and Y. slope coefficient of the regression line. intercept of the regression line with the Y-axis. predicted value of Y from knowing X.
- Suppose that you have the following three regression models: Yi B₁ + B₂x₁ + Uj regression) Y₁ = a₁ + a₂x₁ + eį, if i is male male individuals) Yi = ₁ + ₂x₁ + Ei, if i is female (separate regression for female individuals) ESS RSS The error terms satisfies that E[ui] = E[ei] = E[ei] = 0. Then, we find the following RSS and ESS: Pooled Regression 124.3 25 (separate regression for (pooled 71.1 11.4 separate separate regression for regression for male individuals female individuals 56.6 8.6 The number of sample size is given by 18. Select the correct statement(s). The RSS from the pooled regression is always smaller than the sum of RSSS from the separate regression models. In the above setup, Chow test is equal to 2. If e; is correlated with €;, then the OLS estimator of a2 from the separate regression will be is biased. If the variances of e; is different from €;, then the OLS estimator of 3₂ is no longer unbiased estimator. If we add another variable z; to the pooled regression, then the…The estimated regression equation for a model involving two independent variables and 10 observations follows. ý = 29.1370 + 0.5103x, + 0.4980x2 (a) Interpret b, in this estimated regression equation. O b, = 0.5103 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 29.1370 is an estimate of the change in y corresponding to a 1 unit change in x, when x., is held constant. O b, = 0.4980 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 0.4980 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 0.5103 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. Interpret b, in this estimated regression equation. O b, = 0.4980 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 0.4980 is an estimate of the change in y corresponding to a…6- For one of the simple linear regression model Σ(iyi) = 150 and ² = 50. Find slope coefficiem B₁. (Please be careful x and y are lower letters) 10 3 8 5 0,33 18032
- he 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 isA linear regression equation has b = -4 and a = 8., X = 2? is it Ŷ = 0?It has been hypothesized that overall academic success for first-year college students as measured by grade point average (GPA) is a function of IQ scores = X1, and hours spent studying each week = X2. Suppose the regression equation is: Y = -5.7 + 0.02X1 +0.5X2 1) What is the predicted GPA for a student with an IQ of 100 and 40 hours spent studying per week? 2)Will the independent variables be endogenous? State what it means by endogenous, and explain why that will be the case. 3) If you have a choice to change the variables or add/drop variables, what would be your set of independent variables, and explain why you chose those variables.
