Question 1 A multiple regression was performed of y = life expectancy at birth on X1 = mean years of schooling of adults over the age of 25, X2 = GDP per capita (gross domestic product in constant 2005 international $), and X3 = carbon dioxide emissions per capita (tonnes) for 31 countries. The data were obtained from the human development website http://hdr.undp.org/en/. Based on the following ANOVA table, calculate raaj Source DF SS MS F P-Value Regression 3 498.98 166.33 24.16 0.000 Residual (Error) 27 185.88 6.88 Total 30 684.86 O 76.3% 0 69.8% O 73.7% O Cannot be determined from the information given.W Based on the information in the ANOVA table, how many independent variables are in this regression? Source DF 55 MS F P-Value Regression 3 14.001 4.67 0.484 0.695 Residual[Error) 41 395.629 9.649 Total 44 409.630 0 3 O 41 O 44 O 2 Question 3 Consider the following scatter plot. What can you conclude from this graph? 0 The dependent and independent variable have a linear relationship 0 The dependent and independent variable have a non-linear relationship 0 The dependent and independent variable have a positive linear relationship 0 The dependent and independent variable have a negative linear relationship Question 4 Consider the following normal probability (QQ) plot. Normal Probability Plot 25mm 2m m)...' H ' 0 20 ID 60 ED 100 120 Sam Formula What would you conclude about this data? 0 This data is perfectly normal 0 The data appears to be slightly askew from normal 0 The data is linear o The data follows a Poisson distribution Question 5 Does the following residual plot indicate any violation of the regression assumptions? If so, which one? O Zero-mean O Constant variance 0 Independence O No violation Set up 1. Are more selective colleges more expensive? This is a question asked by students enrolled in a statistics course at a liberal arts college. To answer this question, the students collected information on a random sample of 41 liberal arts colleges across the nation. They considered the regression model given below. ,um = so + 31 PRIVATE + 32 ADM_RATE ariable II escription COST * verage cost of attendance Below is the output the students obtained from their favorite statistical software package. _33670.89 5486.87 6.137 R2 = 0.6009 Adj.Rz = 0.5799 s = 8364 What is the interpretation of the estimated slope associated with PRIVATE? O For each 1-unit increase in private, the average cost of attendance increases by $22,713.66, holding the admissions rate constant. 0 The average cost of attendance fora private school is $22,713.66 higher than the average cost for a public school, assuming that they have the sarr admissions rate. 0 Private schools are $22,713.66 more expensive, on average. 0 None of the answers is correct. Use Set up 1. A plot of the residuals versus fitted values is given below. What does this plot reveal about the appropriateness of the assumptions necessary for inference? 10000 Residual 10000 20000 - 25 50 75 100 Admissions rate O The plot is not useful since it just looks like random scatter. O The spread of the residuals is not constant across admissions rate. O The spread of the residuals is constant across admissions rate. O There are many troubling outliers. Question 8 1 Use Set up 1. If all assumptions necessary for inference are valid and we wished to determine the overall utility of the model, what hypotheses should we test? O Ho: B2 = 0 versus H1: B2 0 O Ho: B1 = 0 versus H1 : B1 > 0 O Ho: B1 = $2 = 0 versus H, : at least one B, # 0 O Ho: B1 = B2 = 0 versus H,: at least one B; > 0You are interested in starting a specialty coffee shop, but you need to establish how the volume of production will affect your average total costs before you can complete your business plan. You have a friend with connections in the industry, and she obtains the average total cost per cup for a random sample of several establishments in your region. The nal data set your friend compiles contains information on 61 coffee shops including the average total cost of production (in cents per cup) and the rate of output (in cups per hour).The regression output for this simple linear regression model is given below. 150 I 3 I25 - 8 u '5 g to:- - 0 {'3 ' o g\" 75- 9