Exam 1

  1. Question

    For 60 firms the number of employees X and the amount of expenses for continuing education Y (in EUR) were recorded. The statistical summary of the data set is given by:
    Variable X Variable Y
    Mean 56 259
    Variance 113 1792
    The correlation between X and Y is equal to 0.52.
    Estimate the expected amount of money spent for continuing education by a firm with 62 employees using least squares regression.

    Solution

    First, the regression line yi = β0 + β1 xi + ϵi is determined. The regression coefficients are given by:
    β ^ 1 =r· sy sx =0.52· 1792 113 =2.07078, β ^ 0 = y - β ^ 1 · x =259-2.07078·56=143.03654.

    The estimated amount of money spent by a firm with 62 employees is then given by:
    y ^ =143.03654+2.07078·62=271.425.