Diploma in Statistics Introduction to Regression Lecture 4.11 Introduction to Regression Lecture 4.2 Indicator variables for estimating seasonal effects in time series –another application, Meter Sales analysis Correlated explanatory variables

Diploma in Statistics Introduction to Regression Lecture 4.12 Housing Completions case study

Diploma in Statistics Introduction to Regression Lecture 4.13 Table 1.7 Completions and Quarterly Indicators

Diploma in Statistics Introduction to Regression Lecture 4.14 Model formulation Completions =  1  Q 1 +  2  Q 2 +  3  Q 3 +  4  Q4 +   Time + . Quarter 1:Completions =  1 +   Time Quarter 2:Completions =  2 +   Time, Homework 4.1.1:Write down the prediction formulas for future third and fourth quarters.

Diploma in Statistics Introduction to Regression Lecture 4.15 Prediction formula Predicted completions = 3,248  Q  Q  Q  Q  Time  500 Exercise:Write down separate prediction formulas for each of the four quarters. Make predictions for each quarter of 2001 and of 2002.

Diploma in Statistics Introduction to Regression Lecture 4.16 A sales forecasting problem Southern Oil Products vegetable oil producer raw material supply is seasonal, variety of sources / countries problems in second quarter of last year prompts business review forecasts required for –budgetting and staff planning –quantifying extent of last year's problem

Diploma in Statistics Introduction to Regression Lecture 4.17 Table 9.1Quarterly production of vegetable oil, in numbers of 50 litre drums, for a six year period

Diploma in Statistics Introduction to Regression Lecture 4.18 Initial data analysis

Diploma in Statistics Introduction to Regression Lecture 4.19 A simple linear model for trend (Years 1-5) Regression Analysis: Production versus Time The regression equation is Production = Time Exercise: Estimate quarterly/annual growth in production Predictor Coef SE Coef T P Constant Time Exercise: Calculate a confidence interval for quarterly/annual growth in production S = Exercise: Comment on prediction

Diploma in Statistics Introduction to Regression Lecture Quarterly indicator variables Special variables Q1, Q2, Q3 and Q4 called indicator variables may be added to the simple regression model to produce a multiple regression model incorporating the seasonal effects. Each quarterly indicator takes the value 1 in the relevant quarter and 0 otherwise. Note that, in each row, only one of the quarterly indicators takes the value 1, while the other three take the value 0. Thus, for each time (row), the indicator with value 1 indicates the corresponding quarter, 1, 2, 3 or 4

Diploma in Statistics Introduction to Regression Lecture Table 9.2 Quarterly production of vegetable oil, in numbers of 50 litre drums, with Time and quarterly indicators, for a five year period

Diploma in Statistics Introduction to Regression Lecture Multiple regression model Production =  1  Q 1 +  2  Q 2 +  3  Q 3 +  4  Q 4 +   Time + .

Diploma in Statistics Introduction to Regression Lecture Regression Analysis Production vs Q1, Q2, Q3, Q4, Time The regression equation is Production = 1030 Q Q Q Q Time Predictor Coef SE Coef T P Noconstant Q Q Q Q Time S =

Diploma in Statistics Introduction to Regression Lecture Exercise Predict the first quarter production levels for Year 6 and Year 7 Comment on prediction error with respect to (i) its previous vale (ii) recent production levels Next: Diagnostic analysis

Diploma in Statistics Introduction to Regression Lecture Exercise Following calculation of a revised regression, make a table of initial and revised coefficient estimates and residual standard deviations. Compare. Which would you choose? Why?

Diploma in Statistics Introduction to Regression Lecture Exercise Confirm and quantify the extent of the problem in Year 6, Q2. Homework Confirm and quantify the extent of the recovery in Year 6, Q3.

Diploma in Statistics Introduction to Regression Lecture Multiple regression model, alternative formulation Production =  1  Q 1 +  2  Q 2 +  3  Q 3 +  Time  Time + .

Diploma in Statistics Introduction to Regression Lecture Alternative regression * Q4 is highly correlated with other X variables * Q4 has been removed from the equation. The regression equation is Production = Q Q Q Time Predictor Coef SE Coef T P Constant Q Q Q Time S =

Diploma in Statistics Introduction to Regression Lecture Homework List correspondences between the output from the original regression and the output from the alternative regression. Confirm that the coefficients of Q1, Q2 and Q3 in the original are the corresponding coefficients in the alternative with the Q4 coefficient added.

Diploma in Statistics Introduction to Regression Lecture Introduction to Regression Lecture 4.2 Indicator variables for estimating seasonal effects in time series –another application, Meter Sales analysis Correlated explanatory variables

Diploma in Statistics Introduction to Regression Lecture Another application, meter sales analysis Recall the analysis of Meter sales, discussed in Lab 1 Feedback.doc.

Diploma in Statistics Introduction to Regression Lecture Another application, Meter Sales analysis Meter Sales jumped when nominal Phone Charge increased. Model these jumps by adding "indicators" defined to be 0 for all years prior to the jump and 1 for all years during and after the jump. Thus, the first jump occurred during 1952, so the corresponding indicator will be 0 from 1949 to 1952 and 1 from 1953 to Multiplying this explanatory variable by regression coefficient  adds 0 to predicted Meter Sales from 1949 to 1952 and adds  from 1953 to 1983.

Diploma in Statistics Introduction to Regression Lecture Another application, Meter Sales analysis Regression Analysis: Meter Sales versus GNP, RLP,... Predictor Coef SE Coef T P Constant GNP RLP RPC Jump Jump Jump Jump S =

Diploma in Statistics Introduction to Regression Lecture Another application, Meter Sales analysis Note that the t-value for RPC is negligible so that RPC may be omitted. The variation explained by RPC is captured by the four indicator variables. Also, the s value is lower than before, suggesting that the variation in Meter Sales is better explained by the indicators than by RPC alone. N.B.Additional uses for indicators may be found in Extra Notes, Indicators.doc

Diploma in Statistics Introduction to Regression Lecture Introduction to Regression Lecture 4.2 Indicator variables for estimating seasonal effects in time series –another application, Meter Sales analysis Correlated explanatory variables

Diploma in Statistics Introduction to Regression Lecture Correlated explanatory variables Ref:Extra Notes Homework Calculate the simple linear regressions of Jobtime on each of T_Ops and Units. Confirm the corresponding t-values. Calculate the simple linear regression of Jobtime on Ops per Unit. Comment of the negative correlation of Jobtime with Ops per Unit in the light of the corresponding t-value. Confirm the calculation of the R 2 values.

Diploma in Statistics Introduction to Regression Lecture Reading SA §§ Hamilton, pp 82-84,