*Introduction to Statistical Reasoning*

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

( HW_4_1) Can an estimator be unbiased, but imprecise? For the following data what is an unbiased estimator of the population mean? Compute the correspondingestimate[the sample average] and itsprecision[StdError(sample avg.)].

2 | 5 | 9 | 2 | 3 | 7 | 11 | 2 | 3 | 6 | 4 | 4 | 7 | 6 | 6 | 10 | 4 | 3 | 5 | 7 |

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**HW_4_2**) Compute the correlation coefficient,**R(X,Y)**, for the following data. Please do this by hand and show all of your work. Find a linear equation which describes the best linear regression fit (*least squares fit*) ofon**Y**.*X*

X | Y |

1 | 0 |

3 | 1 |

5 | 4 |

7 | 7 |

9 | 8 |

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**HW_4_3**) 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}?