x>0 f(x) = 8² elsewhere Find the value of c such that an interval from x to cx is a (1- a)100% confidence interval for the parameter 8.
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- Suppose that n = 50, i.i.d observations for (Y₁, X₁) yield the following regressions results: Ỹ= 49.2 + 73.9 X, SER = 13.4, R²=0.78 (23.5) (16.4) Another researcher is interested in the same regression, but makes an error when entering the data into a regression program: The research enters each observation twice, ending up with 100 observations (with observation 1 entered twice, observation 2 entered twice and so forth). Using these 100 observations, what results will be produced by the regression program? Complete the spaces in the equation below. Report the intercept and slope to one decimal place, but report the R2 to two decimal places. Ŷ = + * X, R² =Book Pages (x) Price (y) A 500 $7.10 B 700 7.60 C 750 9.10 D 590 6.60 E 560 7.60 F 650 7.10 G 475 5.10 (a) Develop a least squares estimated regression line. (Round your numerical values to three decimal places.) (b) Compute the coefficient of determination. (Round your answer to four decimal places.) Explain its meaning. (Give your answer as a percent. Round your answer to two decimal places.) The value of the coefficient of determination tells us that % of the variability in |--?-- ☑ has been explained by the least squares regression equation.1) What is the slope(b1) and what is its statistical interpretation? 2) Perform the test of hypothesis (t-test) on the following and state your statistical decision. Use α = 0.01. Please show all the relevant calculations. H0: β1 = 0 H1: β1 ≠ 0 3) Perform the test of hypothesis (F-test) on the following and state your statistical decision. Use α = 0.01. Please show all the relevant calculations. H0: β1 = 0 H1: β1 ≠ 0 4) What is the coefficient of determination (r2) i.e., percentage of variability in the monthly rent explained by the independent variable rental property area? Please show all the relevant calculations. 5) What is the 99% confidence interval for the population slope(β1)? Please show all the relevant calculations.?
- X= 80, Me = 70, Lower Quartile (Qı) = 20, Upper quartile (Q3) = 100 and S.D From the data given below, ascertain (1) Pearson's Coefficient of Skewness, and (11) Bowley's Coefficient of Skewness %3D %3D %3DtySuppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?
- Find the least square regression line.1assessment.casa.uh.edu/Assessment/Root/Pages/TestTaker/Quiz.aspx?id=2F507231-0111-4CFC-8C26-F38ED05C3949 f) O None of the above Review Later Question 7 If the LSRL relating the independent variable x and the dependent variable y for a given problem is ŷ = 2x + 4, then an increase of 1 unit in x is associated with an increase of how many units in y? a) 06 b) 00 d) O1 e) 04 Review Late
- Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 139 to 188 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.62 cm, y = 81.37 kg, r 0.113, P-value = 0.263, and y = - 105+1.01x. Find the best predicted value of y (weight) given an adult male who is 142 cm tall. Use a 0.05 significance level. %3D The best predicted value of y for an adult male who is 142 cm tall is kg. (Round to two decimal places as needed.)With t test statistics and its p-value, given in the regression output, we test: O a. a joint hypothesis about significance of all parameters except constant O b. a single hypothesis about insignificance of R^2 O C. a single hypothesis about significance of parameter O d. a joint hypothesis about insignificance of all regression parametersSuppose that n = 100 i.i.d. observations for (Y, X) yield the following regression results: Ŷ 32.1 + 66.8X, SER = 15.1, R² = 0.81. = (15.1) (12.2) Another researcher is interested in the same regression, but he makes an error when he enters the data into his regression program: He enters each observation twice, so he has 200 observations (with observation 1 entered twice, observation 2 entered twice, and so forth). a. Using these 200 observations, what results will be produced by his regression program? (Hint: Write the "incorrect" values of the sam- ple means, variances, and covariances of Y and X as functions of the "correct" values. Use these to determine the regression statistics.) Ŷ - X, SER = 6tc () () b. Which (if any) of the internal validity conditions are violated?