*Introduction to Statistical Reasoning*

http://www.stat.ucla.edu/~dinov/ |

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**HW_3_1**) Compute the correlation coefficient,**R(X,Y)**, for the following data. Interpret your result. Please do this by hand and show all of your work. Find a linear equation, a line l_{o}, which describes the best linear regression fit (*least squares fit*) ofon**Y**. If we have two other candidate lines, l*X*_{1}and l_{2}, each with residual square error (RSE ) of 123 and 153, respectively. Compute the RSE for the best (least squares) line you computed, l_{o}, and rank the three lines best to worst fit. What is your ranking criterion?

X | Y |

1 | 0 |

3 | 1 |

5 | 4 |

7 | 7 |

9 | 8 |

What is the correlation R(Y, X)? R(3X-2.2 , -4Y +7)?

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**HW_3_2**) Find the equation of the line, l_{1}, passing through the points (-3, 5) and (1, 2). Identify the**slope**, m_{1}, and Y-**intercept**, b_{1}, of the line. A line, l_{2}, is*perpendicular*to l_{1}if its**slope**is -1/m_{1}. Find the equation of the line, l_{2},*perpendicular*to l_{1}, which goes through the point (X=0, Y=3). What are l_{2}'s**slope**, m_{2}, and Y-**intercept**, b_{2}?