Question: A response variable has two possible explanatory variables, X₁ and X₂. Three linear models are produced - one based on X₁ only, one based on X₂ only, and one based on both X₁ and X₂. The AIC values for each model respectively are, 178.45, 183.56, and 149.21. Which is the best model based on the AIC value? A: Based on X₁ only. B: Based on X₂ only.. C: Based on X₁ and X₂. D: Can't be sure. 13

Please use linear regression test statistics, and defined everything -- all parts.

To perform a test to determine whether we have a significant linear relationship using an F test, your friend tells you to compute a two-sided p-value. Is this correct and why?

A random sample of 136 adults were asked to report the number of hours per week the spent on a computer and their number of years of education. The linear model equation below describes the relationship between the mean computers hours and years of education. computers == 9.12 ++ 0.8 ×× education Based on this linear model, which of the following statements is correct? a) An adult who has no years of education is expected to spend 9.12 hours per week on a computer. b) An adult who has 1 more year of education than another is expected to spend 9.12 more hours per week on a computer. c) An adult who spends 1 more hour per week on a computer than another is expected to have had 9.12 more years of education. d) An adult who spend zero hours per week on a computer is expected to have 9.12 years of education.

The owener of a winery collects data on competing wineries every year.  He would like to predict the gross sales (in number of cases) from the size of the wineries (in acres). What is the explanatory variable in this study?

The relationship between IQ level and exam score was estimated as below in a linear format. (IQ level and exam scores are both measured in points)   Exam score = 1.38 * IQ level - 67.43 (The p-value for the coefficient of IQ level is 0.04.)   Base on the above equation, which of the following statements are true? (Select all that apply. There can be more than one answer.) The expected exam score of a person with an IQ level of 100 points is 70.57 The expected exam score of a person with an IQ level of 0 points is 1.38 points As a person’s IQ level increases by 1 point, his or her exam score is expected to increase by 1.38

Consider the model y=-2.45x+7.18 derived from data between x=4 and x=10. What value of x represents interpolation of the data?

Suppose that 95% of the bags of certain fertilizer mix weigh between 49 and 53 pounds. Averages of three succesive bags were plotted, and 47.5% of these were observed to lie between 51 and X pounds. Estimate the value of X. State assumptions you make and say whether these assumptions are likely to be true for this example.

The data used is from college campuses. The variables used in the analysis below include: crime, total campus crime; enroll, total enrollment; police, employed officers. Use the estimated OLS models to answer the questions below: Model A: In(crime) = -6.631 + 1.270ln(enroll), (1.034) (.110) .5804 n = 97; R² = Model B: In(crime) = -4.794+.923ln(enroll) +.516ln(police), (.144) (.149) (1.112) n = 97; R² = .632 Using Model A, test the null hypothesis that elasticity of crime with respect to enrollment is unit elastic, i.e. equal to one (against a two-sided alternative). What is the conclusion of your test using a significance level of .01? Reject Fail to reject O Not enough information.

Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables?    (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly.     (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly.       (d) Suppose a second regression model (Model 2) was generated using only…