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Correlation and Linear Regression

It is widely believed that the more education one receives the higher the income earned at the time of first employment and over the course of a career. However, due to varying reasons, many people never complete high school and, thus, never receive their high-school diploma. Although individuals without a high-school diploma are often able to find employment, they experience economic outcomes quite different from those who finish high school before entering the workforce to earn a living. Across the nation, there are millions of individuals with families who are now working but do not possess the credentials of a high-school diploma. Many of these individuals and their families are considered to be a part of the working poor that make up a considerable portion of this nation's labor force.

1. Use technology to creat and provide a scatterplot of the association between the "percent of low-income working families" and the "percent of 18-64 yr-olds with no high school diploma" data for each jurisdiction. Writ at least two sentences explaining how/why it is appropriate to create such a scatterplot, and describe the characteristics of the association seen in the scatterplot. Be sure to use the actual names of the variables in their appropriate places in your response(s). (Print or copy-and-paste the scatterplot and be sure to clearly identify the predictor and response variables based on the possible believed association.)

2. Use technology to find the regression equation for the linear association between the "percent of low-income working families" and the "percent of 18-64 yr-olds with no high school diploma." (Round final values to two decimal places.) Provide this equation and wrie a brief interpretation of the slope using the variable names. (Print or copy-and-paste the printout that identified the equation of the linear regression line, or any other form of evidence that technology was used.)

3. A student states that a decrease in the "percent of 18-64 yr-olds with no high school diploma" will lead to a decrease in the "percent of low-income working families." Writ at least two concise sentences addressing the key uses of linear correlation and comment on its limitations in a response to the student's statement.

4. Calculate and provide the R-squared value for the regression equation. Provide a statement about its meaning, in general, and, its specific interpretation in the context of this assignment.

5. After examining these data for all the jurisdictions, someone notes that certain areas have an unusually high "percent of 18-64 yr-olds with no high school diploma." Based on this finding, this individual concludes that the high percentages are due to the rising population of immigrants in those areas. Further, the individual argues that any estimates of the associated "percent of low-income working families" in those areas should be recalculated after removing this sub-population from the data set, as they are causing the area to "look bad". In addition to thinking critically, use the key rules about linear regression and extrapolation to wrie a statistically appropriate and socially responsible response to the individual's conclusion and argument.

uansition probabilities. If it is not, tell why not. 5. A Markov chain {Xn, n > 0) with states 0, 1, 2, has the transition probability matrix 0 -IN 0 -IN -Im -/m O -10 N/m -IN If P{Xo =0} = P{Xo = 1} = 4, find E[X3]. Let the transition probability matrix of a two-state Markov chain be given, as(1 mark each) For each of the given matrices, select all decompositions that can be applied to it. You do not have to show your work for this question. 2 ) A = [61 O Diagonalization (i.e., A = PDP-1 with D diagonal) O Schur triangularization O Spectral decomposition O Singular value decomposition b ) B = 0 1.001 Diagonalization O Schur triangularization O Spectral decomposition Singular value decomposition c) C is the 75 x 75 matrix with every entry equal to 1. Diagonalization Schur triangularization O Spectral decomposition Singular value decomposition d) D = 0 1 1 Diagonalization OSchur triangularization Spectral decomposition Singular value decompositionE. A Markov chain with the states 1, 2, 3 has transition probability matrix: 1 2 3 1 0.3 a 0.7 P = 2 0.4 0.3 b 3 c 0.2 [3.7 [3.] Give the values of o, b, and c that make the above a valid transition probability matrix. {3 points) (b) The 2-step transition probability matrix is 0.16 0.14 0.70 P12}: 0.2? 0.15 0.53 0.13 0.20 0.62 If the initial distribution of states is P0 = (0.3, [L7, [I], calculate the distribution of the states after 2 transitions. (3 points) (c) Will this Markov chain have a steady state distribution? Justify your mlswer. (2 points)