Solution Manual for A Second Course in Statistics Regression Analysis 6th Edition by William Mendenhall and Terry L. Sincich

Chapter 3 3.2 Since the line passes through the point (0, 1), 1 = β0 + β1(0) ⇒ β0 = 1 And since it also passes through the point (2, 3), 3 = β0 + β1(2) = 1 + 2β1 ⇒ 2 = 2β1 ⇒ β1 = 1 ⇒ y = 1 + x 3.4   3.6 Summary calculations yield: ∑x= 21 ∑x2 = 91 = 3.5 ∑y = 18 ∑y2 = 68 y = = 3 ∑xy= 78 a. SS xx = 1 ! n( x ) 2 = 91 ! 6(3.5)2 = 91 ! 73.5 = 17.5 SS xy = 2 ! n x y = 78 ! 6(3.5)(3) = 78 ! 63 = 15 βˆ 1 = SS xy = 15 = .8571 b. 3.8 a. The straight-line model is y = β0 + β1 x + ε. b. Yes. The data form a rather straight line from the lower left of the plot to the upper right. c. The fitted model is yˆ = 20.9 + 1.07x. ˆ d. β 0 = 20.9. The mean sale price when the appraised value is 0 is estimated to be 20.9 or $20,900. Since x = 0 (appraised value = 0) is not in the observed range, this value has no meaning. ˆ e. β 1 = 1.07. For each unit ($1,000) increase in appraised value, the mean sale price is estimated to increase by 1.07 ($1,070). f. $300,000 ⇒ x = 300 yˆ = 20.9 + 1.07(300) = 341.9. The estimated mean sale price for a house appraised at $300,000 is $341,900. 3.10 a. Yes. For the men, as the year increases, the winning time tends to decrease. The straight-line model is y = β0 + β1x + ε. We would expect the slope to be negative. b. Yes. For the women, as the year increases, the winning time tends to decrease. The straight-line model is y = β0 + β1x + ε. We would expect the slope to be negative. c. Since the slope of the women’s line is steeper that that for the men, the slope of the women’s line will be greater in absolute value. d. No. The gathered data is from 1880 to 2000. Using this data to predict the time for the year 2020 would be very risky. We have no idea what the relationship between time and year will be outside the observed range. Thus, we would not recommend using this model. 3.12 a. The equation for the straight-line model is y = β0 + β1x + ε. b. Some preliminary calculations are: