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Texas Weather Example Multiple Linear Regression

Texas Weather Example Multiple Linear Regression. Data. Response (Y) – Average January High Temp Predictors: Latitude Elevation Longitude Units – n=16 County Weather Stations. Estimating the Full Model. Temp = b 0 + b 1 LAT + b 2 ELEV + b 3 LONG + e. Testing the Full Model.

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Texas Weather Example Multiple Linear Regression

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  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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