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Multiple Linear Regression Analysis of Texas County Weather Stations

This study utilizes multiple linear regression to analyze the average January high temperatures across 16 Texas county weather stations. The model includes latitude, elevation, and longitude as predictors. The hypothesis testing indicates that latitude has a significant impact on temperature, while elevation and longitude do not show significant relationships at the 0.10 level. The paper compares the complete model to a reduced model, confirming that latitude is essential in determining temperature but suggests that elevation and longitude may not contribute significantly after controlling for latitude.

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Multiple Linear Regression Analysis of Texas County Weather Stations

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Presentation Transcript

  1. Texas Weather ExampleMultiple Linear Regression

  2. Data • Response (Y) – Average January High Temp • Predictors: • Latitude • Elevation • Longitude • Units – n=16 County Weather Stations

  3. Estimating the Full Model • Temp = b0 + b1LAT + b2ELEV + b3LONG + e

  4. Testing the Full Model • H0: b1 = b2 = b3 = 0 • HA: Not all bi = 0 • TS: Fobs = MSR/MSE = 491.138 • P-Value: P(F≥491.138)  0

  5. Testing Individual Partial Coefficients • H0: bi = 0 HA: bi≠ 0 TS: tobs = bi/SE(bi) • Latitude: tobs = -14.61 P-value  0 • Elevation: tobs = -1.68 P-value = .1182 • Longitude: tobs = -1.68 P-value = .1182

  6. Comparing Regression Models • Note: Controlling for ELEV and LAT, LONG does not appear significant (at a=.10 level) and same result holds for LONG. • Test whether after controlling for LAT, neither ELEV or LONG related to TEMP • H0: b2 = b3 = 0 HA: b2and/or b3≠ 0 • Complete Model: • Temp = b0 + b1LAT + b2ELEV + b3LONG + e • Reduced Model • Temp = b0 + b1LAT + e

  7. Complete and Reduced Models

  8. Test of H0: b2 = b3 = 0 • SSRc = 934.328, SSEc = 7.609 • SSRr = 881.003 • N=16, k=3, g=1

  9. Model with Latitude and Elevation • Temp = b0 + b1LAT + b2ELEV + e

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