Correlation and regression and time series analysis - Lab Report Example

Correlation and regression and time series analysis. Data: Data on household consumer expenditure in the UK from 2000 to 2008. The data was collected on a quarterly basis and measured in million pound (). All of the data are measured in current prices but are not seasonally adjusted. The data was downloaded from http://www.statistics.gov.uk/statbase. Variables: The following variables were used during the analysis: Consumer Expenditure on Food and non-alcoholic beverages, measured in million Consumer Expenditure on Alcoholic beverages and tobacco, measured in million Consumer Expenditure on Clothing and Footwear, measured in million Consumer Expenditure on Housing, water, electricity, gas and other fuels in million Consumer Expenditure on Furnishings, household equipment and routine maintenance in million Consumer Expenditure on Transport in million Household final consumption expenditure in million Best Predictor of Household Final Consumption Expenditure: By calculating the correlation coefficients, it was found that consumer expenditure on Housing, water, electricity, gas and other fuels have the highest positive correlation (0.948) with Household final consumption expenditure.

Thus this high correlation concluded that expenditure on household utilities is the best predictor for the Household final consumption expenditure. The high correlation between both variables indicates that when expenditures on household utilities increase, total household expenditures increase accordingly. The opposite is true. Scatter Diagram: Using this "best predictor" and the "Household final consumption expenditure: The following Scatter diagram shows the relationship between the two variables: "Household final consumption expenditure" and "Household and Utilities Expenditures" Figure 1: Scatter Diagram Relationship between Household Expenditures and House and Untilies Correlation Coefficient: Consumer expenditure on Housing, water, electricity, gas and other fuels have the highest positive correlation (0.948) with Household final consumption expenditure as shown in Appendix 1.

Regression Equation: The following regression equation was derived from results in appendix 2. Total Household Expenditures = -14600.2 + 18.7301 * expenditures on household utilities. The positive value of the coefficient indicates the positive correlation between both variables. Prediction Example One: If household utilities expenditures = 10000 million Total Household Expenditures = -14600.2 + 18.7301 *10000 = 172700 million In Q4 of 2001, household utilities expenditures was 10490 million and total household expenditures was 168504 million.

This indicates the high accuracy of the regression equation to predict in the current example. Prediction Example Two: If household utilities expenditures = 15000 million Total Household Expenditures = -14600.2 + 18.7301 *15000 = 266351 million In Q4 of 2007, household utilities expenditures was 12794 million and total household expenditures was 225495 million. This indicates the high accuracy of the regression equation to predict in the current example. Time Series Analysis: Figure 2: Graph of Clothing and Footwear Time Series Figure 2 shows the increaseing trend in expenditures on Clothing as time progress.

It also shows the seasonal variation cycle that is repeated on yearly basis. The average annual increase in expenditures on Clothing and footwear is computed to be 2200 million. The average annual increase is calcuated as shown in appendix 3. Appendix 1: Correlation Coefficient between Variables Year Quarter food alcohol+ tobacco Clothing housing+ utilities household goods transport domestic consumption Year 1.000 Quarter -0.063 1.000 food 0.885 0.139 1.000 alcohol+ tobacco 0.748 0.552 0.814 1.000 clothing 0.472 0.762 0.623 0.917 1.

000 housing+ utilities 0.969 -0.020 0.914 0.787 0.551 1.000 household goods 0.777 0.424 0.775 0.942 0.881 0.818 1.000 transport 0.840 -0.088 0.664 0.481 0.168 0.716 0.447 1.000 domestic consumption 0.948 0.243 0.926 0.907 0.712 0.948 0.898 0.755 1.000 Best predictors of household expenditures are year, food, housing and utilities, alcohol and tobacco, and household goods. Appendix 2: Regression of Household consumption and Household utilities expenditures SUMMARY OUTPUT Regression Statistics Multiple R 0.

897901 R Square 0.806226 Adjusted R Square 0.800354 Standard Error 10005.31 Observations 35 ANOVA df SS MS F Significance F Regression 1 1.37E+10 1.37E+10 137.3018 2.65E-13 Residual 33 3.3E+09 1E+08 Total 34 1.7E+10 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -14600.2 16994.3 -0.85913 0.396469 -49175.4 19974.92 -49175.4 19974.92 household goods 18.7301 1.598461 11.71758 2.65E-13 15.47801 21.98219 15.47801 21.98219 RESIDUAL OUTPUT Observation Predicted domestic consumption Residuals 1 149700.2 -3259.19 2 144755.4 4791.552 3 146328.8 6946.224 4 169010.9 -8656.93 5 157435.7 -5371.72 6 154794.8 1613.219 7 158746.8 2531.168 8 181878.5 -13374.5 9 167980.8 -8159.77 10 168411.6 -3293.56 11 168730 -274.

975 12 194071.8 -17064.8 13 171520.8 -5272.76 14 181372.8 -8674.79 15 178619.5 -1724.47 16 205478.4 -18869.4 17 177476.9 -2255.93 18 189351.8 -7868.81 19 186130.2 -1850.24 20 202818.8 -8240.76 21 181841 253.9556 22 189202 94.02655 23 183845.2 8645.835 24 216997.4 -12573.4 25 186635.9 4058.05 26 195982.3 1494.731 27 191730.5 10000.46 28 219301.2 -6421.24 29 189014.7 12424.33 30 200252.7 7498.268 31 198922.9 13733.1 32 225032.7 462.3464 33 195795 16670.

03 34 198304.8 18859.2 35 196544.2 23130.83 Appendix 3: Steps to calculate average annual increase: 1. Annual average expenditures on clotheing and footwear is calculated. 2. Annual increase in average expendituers on clothing and footwear is calculated. 3. The average annual increase is computed.