Data Analysis

 

 

 

 

 

In this exercise, we will generate simulated data, and will then use this data to perform best subset selection.
(a) Use the morn() function to generate a ppoiictor X of length = 100. as well as a noise vector c of length n = 100. (b) Generate a response vector Y of length n = 100 according to the model
= mo + fl1X +62X2 + (las+ r,
where $0. h. and Os are constants of your choice. (c) Use the regsubsetsf) function to perform best subset selection In order to (bocce the best model containing the predictors X, X2 V10. What is the best model obtained according to C,, BIC, and adjusted R2? Show some plots to provide evidence for your answer, and report the coefficients of the best model ob-tained. Note you will need to use the data. tram() function to create a single data set containing both X and Y.
(d) Repeat (c), using forward stepwise selection and also using back-wards stepwise selection. How does your answer compare to the results in (c)? (e) Now fit a lasso model to the simulated data, again using X, X3, . . . , X I° as predictors. Use cross-validation to select the optimal value of A. Create plots of the cross-validation error as a function of A. Report the resulting coefficient estimates, and discuss the results obtained. (f) Now generate a response vector Y according to the model Y = + flat + €, and perform best subset selection and the lasso. Discuss the results obtained.

 

Sample Solution

came to power in 1979 and represented for many, laissez-faire economics and individual self-determination (Steele, 2018). She believed in power of the market, utilizing it to restore the stagnant British economy and moving away from state provided services. In 1979, cuts resulted in reducing the standard rate of tax from 33% to 30%, the top rate from 83% to 60% and finally cutting public spending by 3% (Bolick, 1995). She reduced the amount of public spending, from 50% to 43%. Thatcher felt high taxes discouraged the incentive to work however, effects of tax cuts increased income inequality through as high earners saw ‘the top 10%- did far better, with their incomes increasing from the equivalent of £472.98 in 1979 to £694.83 in 1990’. The uneven distribution of wealth saw the poorest families receive the least. Reductions in public expenditure affected health, education and social services which created a knock-on effect with substantial loss of public sector jobs resulting in decreased spending on goods and services. Privatisation became Thatcher’s most important and long-lasting legacy. She revealed in her memoirs that it was crucial for ‘reversing the corrosive and corrupting effects of socialism’ Parker. In the 1980-90s, due to fiscal pressures, Thatcher’s conservative views on private ownership and public discontent with the current regime saw the privatisation of public owned entities. For example, the sale of just ‘over 50% of shares in BT and the sale of British Energy in 1996’ (Berrington, 1998). Other privatised industries included electricity, gas, British steel, public bus transportation and other public services. As a result, workforces declined as ‘employment in the electricity and gas industries was cut in half’(Edwards, 2017), problems arose in the regulation of private monopolies to prevent abuse of power, however improved ‘economic growth and improved living standards as privatised businesses cut costs, increased service quality’ (Edwards, 2017). Thatcher can be seen as the key instigator of the sweeping shift from traditional to ‘New Public Management’ initiated by public service reforms. NPM involved the adoption of private sector management ideas to improve structures and processes in the public sector. Thatcher who led the 1980s ‘New Right’ administrations, that put a ‘shrinking government and reduced taxation on the agenda’ (Ferlie, 2017). Thatcher also wanted to remove ‘inefficiency in the state bureaucracy and the deprivilege of the civil service’ as she concluded that the public sector was ‘wasteful, overbureaucratic and underperforming’ (Ferlie et al., 1996). Thatcher wanted to identify areas of waste and inefficiency in the government and ‘improve service quality and customer-orientated service’ (Pollitt, 1996) whilst reducin

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