Topic5_M9118_Data_Analytics.pdf

Dr. Ahmed Bakri, Dr. Krisztina Soreg & Mr. Antonio Moya o o 𝑟 𝑟 is ത ത σ(𝑋 − 𝑋)(𝑌 − 𝑌) 𝑟= (𝑛 − 1)𝑠𝑋 𝑠𝑌 ഥ = σ 𝑋 (sample mean of the independent variable (𝑋)) 𝑿 𝑛 ഥ = σ 𝑌(sample mean of the dependent variable (𝑌)) 𝒀 𝑛 𝑆𝑋 = 𝑆𝑌 = ഥ )2 σ(𝑋−𝑋 𝑛−1 (sample standard deviation of the independent variable (𝑋))...

Dr. Ahmed Bakri, Dr. Krisztina Soreg & Mr. Antonio Moya o o 𝑟 𝑟 is ത ത σ(𝑋 − 𝑋)(𝑌 − 𝑌) 𝑟= (𝑛 − 1)𝑠𝑋 𝑠𝑌 ഥ = σ 𝑋 (sample mean of the independent variable (𝑋)) 𝑿 𝑛 ഥ = σ 𝑌(sample mean of the dependent variable (𝑌)) 𝒀 𝑛 𝑆𝑋 = 𝑆𝑌 = ഥ )2 σ(𝑋−𝑋 𝑛−1 (sample standard deviation of the independent variable (𝑋)) σ(𝑌−𝑌ഥ )2 (sample 𝑛−1 standard deviation of the dependent variable (𝑌)) 𝑟 ෡ = 𝒂 + 𝒃𝑿 𝒀 𝒃=𝒓 𝒔𝒚 𝒔𝒙 ഥ - 𝒃𝑿 ഥ 𝒂=𝒀 𝐼𝑓 𝑏 𝑏 𝑋 𝐼𝑓 𝑏 𝑏 𝑋 When 𝑋 = 0, 𝑌෠ = 𝑎. ෡𝑌 ෡𝑌 𝑟 𝑟 ത ഥ𝑌, 𝑠𝑋 𝑋, 𝑠𝑌. ഥ 𝑿 Σ Σ Σ 𝑋ത ഥ 𝑿 Σ 𝑋ത ഥ 𝒀 Σ 𝑌ത ഥ 𝒀 Σ 𝑌ത Σ ഥ 𝑿 ഥ 𝒀 ഥ 𝑿 ഥ 𝒀 ത ത σ(𝑋 − 𝑋)(𝑌 − 𝑌) 𝑟= (𝑛 − 1)𝑠𝑋 𝑠𝑌 𝑟= 17 = (5−1)(2.12)(2.236) 0.89 𝒓𝟐 𝑟 2 =0.892 =0.7921 ෠ 𝑎 + 𝑏𝑋 𝑌= 𝑠𝑦 𝑏 = 𝑟 = 0.89 𝑠𝑥 2.236 ( ) 2.12 = 0.94 ത 𝑋=7 ത − 0.94 8 = −0.56 𝑎 = 𝑌-𝑏 ෠ 𝑌=−0.56 + 0.94𝑋 ෡ =−𝟎. 𝟓𝟔 + 𝟎. 𝟗𝟒𝑿 𝒀 𝑋 = 50 ෡ =−𝟎. 𝟓𝟔 + 𝟎. 𝟗𝟒𝑿 = −𝟎. 𝟓𝟔 + 𝟎. 𝟗𝟒 𝟓𝟎 = 𝟒𝟔. 𝟒𝟒 𝒀 Sx=2 and Sy=6. 35 30 b= -0.989 25 𝑟 20 15 10 5 X 0 0 5 10 15 20 25 30 𝑠𝑋 𝑠𝑌 2 6 = −0.989( ) =-0.3297 → 𝑌෠ 𝑎 𝑏𝑥 𝑌෠ 𝑎 𝑥 𝑎𝑛𝑑 𝑏 100 90 80 Final Exam Grade 70 60 50 40 30 20 10 0 0 1 2 3 4 5 6 Number of Ansences 7 8 9 10 11 𝑌 ̂ 𝑎 𝑏𝑥 𝑌෠ 𝑥 → 𝑌෠ 𝑥 𝑥 𝑥 → 𝑌෠