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example_LR - Stat 2225 Handout Simple Linear Regression...

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Stat 2225 Handout Simple Linear Regression Example Q18.7 on p.614. Does the final exam mark (out of 100) depend on the average amount of time (hours?) one studies? Regression Analysis - Linear model: Y = a + b*X ----------------------------------------------------------------------------- Dependent variable: Mark Independent variable: Time ----------------------------------------------------------------------------- Standard T Parameter Estimate Error Statistic P-Value ----------------------------------------------------------------------------- Intercept 21.5896 2.8354 7.61429 0.0000 Slope 1.8773 0.0965523 19.4433 0.0000 ----------------------------------------------------------------------------- Analysis of Variance ----------------------------------------------------------------------------- Source Sum of Squares Df Mean Square F-Ratio P-Value ----------------------------------------------------------------------------- Model 28612.4 1 28612.4 378.04 0.0000 Residual 7417.2 98 75.6857 ----------------------------------------------------------------------------- Total (Corr.) 36029.6 99 Correlation Coefficient = 0.891143 R-squared = 79.4136 percent R-squared (adjusted for d.f.) = 79.2035 percent Standard Error of Est. = 8.69976 Mean absolute error = 6.97057 Durbin-Watson statistic = 1.83777 (P=0.2077) Lag 1 residual autocorrelation = 0.0778892 Plot of Fitted Model Time Mark 0 10 20 30 40 50 0 20 40 60 80 100 Estimated regression line (least square line): = 21.6 + 1.9x. y ˆ Page 1 of 3
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