2. (6 points) Check the conditions for inference using the residual plot. Do they seem to be met? List each condition and state why or why not. 3. (16 points) Choose one the explanatory variables and perform a complete individual $t$ test for it's $\beta$ coefficient in the model. Use a significance level of 0.01. Your test write-up for the test should include: a. (2 point) The question of interest (think about what you are testing). b. (4 points) The hypotheses. c. (2 point). The test statistic, $t$. d. (2 point) The degrees of freedom. e. (2 point) The p-value. f. (4 points) A conclusion about the question of interest.
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- Linearity: Check if the residuals are randomly scattered around zero. If there is a clear pattern or curvature in the residuals, the linearity assumption may not be met. - Independence: Check if the residuals are independent of each other. Look for any Show moreā¦
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Question 4 (10) a) Two different analytical tests can be used to determine the impurity level in steel alloys. Eight specimens are tested using both procedures, and the results are shown below. Use the Minitab output provided to answer the following questions. (i) Perform a hypothesis test to determine whether the differences between the observations are normally distributed. State your hypotheses, the test statistic, a p-value, the decision made and your conclusion. (ii) Test whether the mean level of impurity for both of the types of alloy are the same or not. State your hypotheses, a p-value, the decision made and your conclusion. Also indicate which output you used to make your decision. Output 5.1: Two-Sample T-Test and CI: Test 1, Test 2 Two-sample T for Test 1 vs Test 2 N Mean StDev SE Mean Test 1 8 1.450 0.220 0.078 Test 2 8 1.662 0.277 0.098 Difference = mu (Test 1) - mu (Test 2) Estimate for difference: -0.212 95% CI for difference: (-0.483, 0.058) T-Test of difference = 0 (vs not =): T-Value = -1.70 P-Value = 0.114 DF = 13 Output 5.2: Probability Plot of Test1-Test2 Normal Mean -0.2125 StDev 0.1808 N 8 AD 0.400 P-Value 0.274 Output 5.3: Paired T-Test and CI: Test 1, Test 2 Paired T for Test 1 - Test 2 N Mean StDev SE Mean Test 1 8 1.4500 0.2204 0.0779 Test 2 8 1.6625 0.2774 0.0981 Difference 8 -0.2125 0.1808 0.0639 95% CI for mean difference: (-0.3636, -0.0614) T-Test of mean difference = 0 (vs not = 0): T-Value = -3.32 P-Value = 0.01
Thuc N.
Part B [TOTAL MARKS: 45] Question 1 [CLO4] [18 marks] Based on the EViews result in Table 1, answer the following questions. Table 1: Estimated Regression Result Dependent Variable: LSDR Method: Least Squares Sample: 2000Q1 2012Q4 Included observations: 52 Variable Coefficient Std. Error t-Statistic Prob. LM2 -0.182046 0.233180 -0.780708 0.4389 LREER -0.389654 0.114675 -3.397895 0.0014 LGDP 0.195732 0.282253 0.693465 0.4914 LTBR -0.001812 0.017134 -0.105733 0.9162 C 3.755816 1.009758 3.719522 0.0005 R-squared 0.602003 Mean dependent var 2.092678 Adjusted R-squared 0.568130 S.D. dependent var 0.153261 S.E. of regression 0.100718 Akaike info criterion -1.661763 Sum squared resid 0.476778 Schwarz criterion -1.474144 Log likelihood 48.20584 Hannan-Quinn criter. -1.589834 F-statistic 17.77280 Durbin-Watson stat 0.567689 Prob(F-statistic) 0.000000 a. Write down the estimated result in the form of equation. [2 marks] b. Examine the parameters of interest from the perspective of statistical significance. (hint: used p-value) [10 marks] c. What is your conclusion about the relationship between parameter of interests based on the empirical results? [2 marks] d. Based on the empirical results in Table 1, what are the possible diagnostic problems that you observe? [4 marks]
Sri K.
QUESTION 13 Put the four steps of the general hypothesis testing procedure in order. Specify the Hypotheses Determine the rejection region (or find the p-value) Make a conclusion Calculate the test statistic QUESTION 14 How does hypothesis testing differ from constructing confidence intervals, in general? Read carefully. A hypothesis test examines the evidence in the data for a specified value of the parameter chosen by the researcher, with the probability of making a Type I error equal to Ī± . A confidence interval gives a range of "reasonable" values for a parameter, and therefore is never wrong. A hypothesis test gives a range of "reasonable" values for the parameter based on a specific set of data, while a confidence interval examines the evidence in the data for a specified value of the parameter chosen by the researcher. A hypothesis test leads to the right decision 50% of the time, while a confidence interval uses a method that is correct (1 - Ī±)100% of the time (ex: 95% of the time). A hypothesis test requires fewer assumptions than a confidence interval, and is also more accurate, for any choice of Ī± . A hypothesis test examines the evidence in the data for a specified value of the parameter chosen by the researcher, while a confidence interval gives a range of reasonable values for the parameter based on a specific set of data.
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