Exercise 9.5 Take the linear model Yi = x'iiß1 + x2iß2 + éj E (Xili) = 0 where both Xli and X2i are qx 1. Show how to test the hypotheses Ho: B, = B, against Hı:ß, # B2.
Exercise 9.19 An economist estimates Yi = xlißi + x2iß2 + ei by least-squares and tests the hypothesis Ho: B2 = 0 against Hı: B2 #0. She obtains a Wald statistic Wn = 0.34. The sample size is n= 500. (a) What is the correct degrees of freedom for the x2 distribution to evaluate the significance of the Wald statistic? (b) The Wald statistic Wn is very small. Indeed, is it less than the 1% quantile of the appropriate x2...
FR2 (4+4+4 12 points) (a) Let XI, X2, X10 be a randoin sample from N(μι,σ?) and Yi, Y2, 10 , Y 15 be a random sample from N (μ2, σ2), where all parameters are unknown. Sup- pose Σ 1 (Xi X 2 0 321 (Y-Y )2-100. obtain a 99% confidence interval for σ of having the form b, 0o) for some number b (No derivation needed). (b) 60 random points are selected from the unit interval (r:0 . We want...
7.97 Suppose you want to test Ho: u = 500 against He: p > 500 using a = .05. The population in question is normally dis- tributed with standard deviation 100. A random sample of size n = 25 will be used. a. Sketch the sampling distribution of x assuming that Ho is true. b. Find the value of xo, that value of x above which the null hypothesis will be rejected. Indicate the rejection region on your graph of...
1. What is the coefficient of determination and why is it important? What does it show us? 2. What is heteroskedasticity, which assumption of the linear model does it violate, and how can we test for it? 3. What is multicollinearity? What problems can it cause to our results? 4. If you decide to scale both your dependent and your independent variable by 100, how will your regression results change? 5. Using N=40 observations, you estimate the following model y...
Suppose you fit the first rder mu ple egression model y = po + β1x1 + a. Test Ho βι-o against h, β1 , 0 Use α-D 05 b. Find a 99% confidence interval for P2 interpret the interval 2x2 + ε to n= 25 data points and obtain the prediction equation y = 37.1 + 1.19x1 + 1 3 2 Th° estimated standard deviations ofthe sampling distributions of βι and P2 are 0.23 and 0.18, espec ve y ....
Suppose that X ~ POI(μ), where μ > 0. You will need to use the following fact: when μ is not too close to 0, VR ape x N(VF,1/4). (a) Suppose that we wish to test Ho : μ-710 against Ha : μ μί are given and 10 < μι. m, where 140 and Using 2 (Vx-VHo) as the test statistic, find a critical region (rejection region) with level approximately a (b) Now suppose that we wish to test Ho...