Question;Assignment 2Name ? Section 10Q1. 2.11 (a):We would expect the variable Y would be linearly related to X but that intercept would be zero.An example of a situation where fitting the model is justified by theoretical or other physical and material considerations is distance traveled (X) as a function of time (Y) where there would be no constant and the line can go through the origin.Q1 2.11 (b):This question is phrased vaguely. ?Show? means use equations (2.14) and (2.15) to prove (2.50).Proof:Q1 2.11 (c):Hint: Either prove that symbolically or create your own data set of X and Y variables, compute the slope estimate and show that the residuals don?t add up to zero. The second option is much easier.Solution: If the model includes a constant, the sum of the residuals is in fact zero, since anything else would disrupt the output of the formula for a regression line with an intercept. If there is no intercept and the line goes through zero, thanQ1 2.11 (d):X = [BLANK1, BLANK2, ?, BLANKn]You choose the sample size nY = [BLANK1, BLANK2, ?, BLANKn].Q1 2.11 (e):By this, it means what hypotheses would you test and what test statistic do you use?H0: BLANKH1: BLANKThe test statistic is BLANK.Q2 2.12 (a):PLOT HEREDoes the plot suggest a linear relationship? BLANKDoes it seem reasonable that the two variables are linearly related? BLANKQ2 2.12 (b):.Replace and with the fitted values from R.What is? BLANKWhat is? BLANKQ2 2.12 (c):A 95% CI for is [BLANK1, BLANK2].A 95% CI for is [BLANK1, BLANK2].Q2 2.12 (d):H0: BLANKH1: BLANKPerform the test and give your conclusion. BLANKQ2 2.12 (e):Answer: BLANKQ2 2.12 (f):The 95% interval estimate for theaverage Sunday circulation of newspapers with daily circulation of 500,000 is [BLANK1, BLANK2].Q3 3.3 (a):Replace each of the estimated coefficients below.Model 1:, where and.Model 2:, where and.Model 3:, where, and.Q3 3.3 (b):Report the p-value from the test of the hypotheses, H0:?0 = 0 versus H1:?0? 0, for each of the three models below:Model 1: p-value = BLANKModel 2: p-value = BLANKModel 3: p-value = BLANKQ3 3.3 (c):Which variable predicts the final score better? BLANKQ3 3.3 (d):Would you use model 1, 2 or 3? BLANKWhat value would serve as the best guess for the final score for this student? BLANKQ4 3.4:I don?t have time to look at 120 data sets and check adjusted R2 values. Instead, answer the question below.Let X1 = [1, 2, 3, 4] and let X2 = [1, 0, 1, 4] be the two independent variables.If Y = [3, 6, 13, 2], then is the adjusted R2 negative? BLANKIf Y = [3, 6, 7, 2], then is the adjusted R2 negative? BLANKIf Y = [3, 6, 1, 2], then is the adjusted R2 negative? BLANKQ5 1:Perform a test to determine whether GDPperCapita is useful in predicting tfr.H0: BLANKH1: BLANKPerform the test and give your conclusion. BLANKThe test you performed is only valid if certain assumptions are met.What assumptions were made when you performed this test? BLANKQ5 2:Suppose you have the model, where is the ith observation of tfr, is the ith observation of GDPperCapita, is the ith observation of contraception, is the ith observation of illiteracyFemale and is the ith error term. Answer the question by stating the appropriate hypotheses and performing the correct test.H0: BLANKH1: BLANKPerform the test and give your conclusion. BLANKQ5 3:Using the same model as in part 2, state the appropriate hypotheses and perform the correct test.H0: BLANKH1: BLANKPerform the test and give your conclusion. BLANKQ5 4:The 99% CI for is [BLANK1, BLANK2].Q5 5:Given these values of the independent variables, a 95%prediction interval for tfr is given by [BLANK1, BLANK2].Q5 6:Given these values of the independent variables, a 95%confidence interval for tfr is given by [BLANK1, BLANK2].AppendixCode goes here.
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