420Pr5 - 1. Consider the following data set: x 0 2 4 6 8 y...

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Unformatted text preview: 1. Consider the following data set: x 0 2 4 6 8 y 110 123 119 86 62 a) Construct a scatter plot. Does the plot suggest that a linear relationship is appropriate? Consider the model Y i = + 1 x i + e i , i = 1, 2, 3, 4, 5, where e i s are i.i.d. N ( , 2 ). x = 20, y = 500, x 2 = 120, y 2 = 52,630, x y = 1,734, ( x x ) 2 = 40, ( y y ) 2 = 2,630, ( x x ) ( y y ) = ( x x ) y = 266. OR X T X = & 120 20 20 5 ( X T X ) 1 = & -- 025 . 1 . 1 . 6 . X T Y = & 1,734 500 b) Find the equation of the least-squares regression line. Add the regression line to the scatter plot. ( y y ) 2 = 861.1. c) What proportion of the observed variation in y values is explained by a straight-line relationship with x ? d) Is regression significant at a 5% level of significance? e) Test H : 1 = 0 vs. H 1 : 1 < 0 at a 5% level of significance. f) Test H : = 100 vs. H 1 : > 100 at a 5% and at a 10% level of significance. g) Construct a 90% prediction interval for the future value of y corresponding to x = 10. Consider the model Y i = + 1 x i + 2 x i 2 + e i , i = 1, 2, 3, 4, 5, where e i s are i.i.d. s are i....
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420Pr5 - 1. Consider the following data set: x 0 2 4 6 8 y...

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