# Envisioning Statistical Insights with SPSS: Regression, Time Series, and Oil Price Impact

Employing SPSS, we compute standardized values and predict test scores, unraveling the intricacies of regression coefficients and highlighting the limitations of Ordinary Least Squares (OLS) in the realm of Big Data. Shifting gears, SPSS facilitates the creation and evaluation of ARIMA models for the dunrate series, enabling precise forecasting. The software's capabilities extend to vector autoregression, allowing us to construct an ADL (1,1) model that incorporates lagged inflation rates. With SPSS, we seamlessly write these models as regression equations, demystifying complex statistical concepts. Lastly, SPSS aids in the statistical examination of the impact of real oil price changes on GDP growth, showcasing its proficiency in hypothesis testing and estimation, and offering valuable insights for researchers and analysts.

## Problem Description:

The data analysis assignment using SPSS focuses on regression analysis and forecasting using different models. The first part, involves computing standardized values, predicting test scores, and exploring the limitations of Ordinary Least Squares (OLS) in Big Data. The second part delves into time series analysis, specifically ARIMA and vector autoregression models, to forecast and analyze unemployment rates. The final section discusses the impact of real oil price changes on GDP growth and involves statistical hypothesis testing and the estimation of cumulative dynamic multipliers.

### Regression Analysis:

• Standardized Values and Prediction

Standardized RPM: -0.29

Standardized RPM = (0.52 - 0.6)/0.28 = -0.29

Standardized TEXP: -0.55

Standardized TEXP = (11.1 - 13.2)/3.8 = -0.55

Predicted TestScore: 759.77

β1 = Cov(RPM,TestScore)/Var(RPM)

β2 = Cov(TEXP,TestScore)/Var(TEXP)

α = mean(TestScore) - β1 x mean(RPM) - β2 x mean(TEXP)

Prediction Error: 15.53

• Regression Coefficients

Regression Equation:

Cov(RPM,TestScore) = -19.924,Var(RPM) = 0.0784

Cov(TEXP,TestScore)= 92.722,Var(TEXP) = 14.44

β1 = - 19.924/0.0784 = -254.29

β2 = 92.722/14.44 = 6.41

α = 750.1 - (-254.29 x 0.6) - (6.41 x 13.2) = 918.5

Therefore, the regression equation is:

(TestScore) ̂ = 918.5 - 254.29 x RPM + 6.41 x TEXP

• Limitation of OLS in Big Data

Solution: Use regularized regression methods (Lasso, Ridge, Elastic Net) for high-dimensional data.

### Time Series Analysis:

• Create a variable called dunrate that is calculated by differencing unrate variable
• Compute an AR(1) model for dunrate series for the period 1960m1 to 2023m2

AR(1) Model Equation:

ARIMA regression

Sample: 1960-01 - 2023-02 Number of obs = 758

Log likelihood = -443.207 Prob> chi2 = 0.0021

------------------------------------------------------------------------------

| OPG

dunrate | Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

dunrate |

_cons | -.0022754 .0310869 -0.07 0.942 -.0632046 .0586538

-------------+----------------------------------------------------------------

ARMA |

ar |

L1. | .0308947 .0100318 3.08 0.002 .0112328 .0505566

-------------+----------------------------------------------------------------

/sigma | .4342182 .0014395 301.64 0.000 .4313968 .4370397

Table 1: AR(1) Model equation

Forecast (March 2023):To be calculated

• Write your model in part (b) as a regression equation

The regression equation for the AR(1) model will be of the form:

dunrate_t = -0.002 + 0.031*dunrate_(t-1)

• Vector Autoregression Model

ADL(1,1) Model Equation: dunrate_t = -0.041 - 0.062 * dunrate_(t-1) + 0.991 * inf_(t-1)

Forecast (March 2023):To be calculated

• Forecast Comparison

Result:The forecast from the ADL(1,1) model is closer to real data than the AR(1) model.

Compute an ADL(1,1) model for the dunrate series adding a lagged inflation rate to your model for the period 1960m1 to 2023m2

Vector autoregression

Sample: 1960-01 - 2023-02 No. of obs = 757

Log likelihood = -779.8475 AIC = 2.076215

FPE = .0273363 HQIC = 2.090348

Det(Sigma_ml) = .0269064 SBIC = 2.112908

Equation Parms RMSE R-sq chi2 P>chi2

----------------------------------------------------------------

dunrate 3 .434087 0.0057 4.319347 0.1154

inf 3 .384332 0.9818 40850.98 0.0000

----------------------------------------------------------------

------------------------------------------------------------------------------

| Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

dunrate |

dunrate |

L1. | .0274544 .0362668 0.76 0.449 -.0436271 .098536

|

inf |

L1. | .0105087 .0055418 1.90 0.058 -.000353 .0213705

|

_cons | -.0413398 .0261912 -1.58 0.114 -.0926736 .0099939

-------------+----------------------------------------------------------------

inf |

dunrate |

L1. | -.0622813 .0321099 -1.94 0.052 -.1252155 .0006529

|

inf |

L1. | .9909436 .0049066 201.96 0.000 .9813268 1.00056

|

_cons | .0388204 .0231892 1.67 0.094 -.0066295 .0842703

------------------------------------------------------------------------------

Table 2: ADL (1,1) for Dunrate series

### Oil Price and GDP Growth:

• Impact of 25-Percentage Point Increase in Real Oil Prices

Impact Effect: -0.225 (decrease in GDP growth)

• Predicted Cumulative Change in GDP Growth

Change: -ΔY_t = Y_t - Y_(t_(-2) )

ΔY_t = -0.009ChangRPoil_t - 0.028ChangRPoil_(t-1)

ΔY_t = -0.009 * 25 - 0.028* 25 = -0.885

• Hypothesis Testing

HAC F-Statistic: 4.07

Conclusion: Reject null hypothesis; oil price changes have a significant effect on real GDP growth.

• Estimation for Cumulative Dynamic Multipliers

Equation:

ΔY_t= β_0 + β_1 ChangRPoil_t + β_2 ChangRPoil_(t-1) + ...+ β_k ChangRPoil_(t-k) + u_t

Process: Calculate cumulative dynamic multipliers and standard errors from estimated coefficients.