## Answers

IQ (Y) | BrainV (X) | X - M_{x} | Y - M_{y} | (X - M_{x})^{2} | (X - M_{x})(Y - M_{y}) |

132 | 816.932 | -45.7225 | 22.55 | 2090.547 | -1031.0424 |

132 | 951.545 | 88.8905 | 22.55 | 7901.521 | 2004.4808 |

90 | 928.799 | 66.1445 | -19.45 | 4375.0949 | -1286.5105 |

136 | 991.305 | 128.6505 | 26.55 | 16550.9512 | 3415.6708 |

90 | 854.258 | -8.3965 | -19.45 | 70.5012 | 163.3119 |

129 | 833.868 | -28.7865 | 19.55 | 828.6626 | -562.7761 |

120 | 856.47 | -6.1845 | 10.55 | 38.248 | -65.2465 |

100 | 878.90 | 16.2455 | -9.45 | 263.9163 | -153.52 |

71 | 865.36 | 2.7055 | -38.45 | 7.3197 | -104.0265 |

132 | 852.244 | -10.4105 | 22.55 | 108.3785 | -234.7568 |

112 | 808.02 | -54.6345 | 2.55 | 2984.9286 | -139.318 |

129 | 790.619 | -72.0355 | 19.55 | 5189.1133 | -1408.294 |

86 | 831.772 | -30.8825 | -23.45 | 953.7288 | 724.1946 |

90 | 798.612 | -64.0425 | -19.45 | 4101.4418 | 1245.6266 |

83 | 793.549 | -69.1055 | -26.45 | 4775.5701 | 1827.8405 |

126 | 866.662 | 4.0075 | 16.55 | 16.0601 | 66.3241 |

126 | 857.782 | -4.8725 | 16.55 | 23.7413 | -80.6399 |

90 | 834.344 | -28.3105 | -19.45 | 801.4844 | 550.6392 |

129 | 948.066 | 85.4115 | 19.55 | 7295.1243 | 1669.7948 |

86 | 893.983 | 31.3285 | -23.45 | 981.4749 | -734.6533 |

SS: 59357.8079 | SP: 5867.0995 |

Sum of *X* = 17253.09

Sum of *Y* = 2189

Mean *X* = 862.6545

Mean *Y* = 109.45

Sum of squares (*SS _{X}*) = 59357.8079

Sum of products (

*SP*) = 5867.0995

Regression Equation = ŷ =

*bX*+

*a*

*b*=

*SP*/

*SS*= 5867.1/59357.81 = 0.09884

_{X}*a*= M

_{Y}-

*b*M

_{X}= 109.45 - (0.1*862.65) = 24.1827

ŷ = 0.09884

*X*+ 24.1827

The value of R is 0.2549.

The value of R^{2}, the coefficient of determination, is 0.065.

**Excel Output**

SUMMARY OUTPUT | ||||||||

Regression Statistics | ||||||||

Multiple R | 0.254932853 | |||||||

R Square | 0.06499076 | |||||||

Adjusted R Square | 0.013045802 | |||||||

Standard Error | 21.52910266 | |||||||

Observations | 20 | |||||||

ANOVA | ||||||||

df | SS | MS | F | Significance F | ||||

Regression | 1 | 579.9092977 | 579.9092977 | 1.25114664 | 0.278039633 | |||

Residual | 18 | 8343.040702 | 463.5022612 | |||||

Total | 19 | 8922.95 | ||||||

Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |

Intercept | 24.18349953 | 76.38157836 | 0.316614294 | 0.75517875 | -136.2882417 | 184.6552407 | -136.2882417 | 184.6552407 |

BrainV (X) | 0.098841994 | 0.088366446 | 1.118546665 | 0.27803963 | -0.08680902 | 0.284493008 | -0.08680902 | 0.284493008 |