Question

mplete the tollowing assignment on a separate piece of paper. Answers suomitted on this assignment sheet will not be accepted. When using technology you must attach all relevant outputs to your assignment. The following data was collected during a study to determine if there is a relationship between the vertical drop of the mountain and the number of trails at the resort in New York State. 1. (1200, 30), (700, so), (700, 24), (1500, 62), (1010, 23), (3350, 67),(400, 15). (1600, 34) a.) Generate the regression equation b.) Determine the correlation coefficient. c) Is there enough evidence to conclude that the slope of the regression line is not zero at the 98% confidence level? Explain. d.) A ski resort in Colorado, Aspen Highlands, has a vertical drop of 3635'. Give two reasons why the model created in this problem cannot be used to make a prediction for the number of trails at Aspen Highlands. ready to become a professional. In order to be successful as a 2. A golfer thinks they are rofessional it is necessary to be able to shoot scores at or below par (there are requirements to be met before being allowed on the tour), and a golfer must be consistent in obtaining those scores. Given below are scores from 16 randomly selected rounds the golfer has posted, with a confidence level of 95% answer the question below. 84, 74, 64, 66, 74, 81, 68, 64, 69, 74, 67, 68, 68, 62, 73,65 In order to make money on the tour a professional golfer needs to make the cut by being consistent over several rounds. Here, consistency will be defined as having a standard deviation of your rounds at or below 4 strokes. Is this golfer consistent enough to meet this criteria?

Answer 1

1) a)

Step 1: Find X-Y and X2 as it was done in the table below X.Y 36000 35000 16800 93000 23230 224450 6000 54400 X.X 1440000 490000 490000 2250000 1020100 11222500 160000 2560000 30 1200 700 700 1500 1010 3350 400 1600 50 62 23 67 Step 2: Find the sum of every column Σ , ΣΥ-305 , Σ , Σ X- 10460 X.Y- 488880 X2 19632600 Step 3: Use the following equations to find a and b ΣΥ . ΣΧーΣχ . ΣΧΥ 305-10632600-10460 . 488880 8.19632600 104602 18.348 n . ΣΧΥ-Σχ . Σ Υ n.ΣΧ2 _ (ΣΧ)2 8 . 488880-10460 . 305 0.015 (10460)2 8.19632600 Step 4: Substitute a and b in regression equation formula 18.348 + 0.015-T y

b)

Step 1: Find X.Y, X2 and Y2 as it was done in the table belovw X.Y 36000 35000 16800 93000 23230 224450 6000 54400 X.X 1440000 490000 490000 2250000 1020100 11222500 160000 2560000 Y.Y 900 2500 576 3844 529 4489 225 1156 1200 700 700 1500 1010 3350 400 1600 30 50 62 23 67 15 34 Step 2: Find the sum of every column to get: Σχ-10460 , ΣΥ-305 , Σ , ΣΧ2-19632600 , ΣΥ 2-14219 X.Y- 488880 X2 19632600 Step 3: Use the following formula to work out the correlation coefficient. 8-488880 10460 305 ะ 0.7252 8 . 19632600-104602·18-14219-3052

c) Asyou cansee that the 98% confidence interval for slope contains zero between them, hence we have no evidence to say that the slope of the regression line is not zero.

50 Regression Statistics Multiple R R Square Adjusted R Squai 0.446970957 Standard Error14.30698691 Observations 0.725241412 0.525975106 1500 1010 3350 62 23 67 15 34 1600 ANOVA Significance F MS Regression Residual Total 1362.735753 1362.735753 6.65756309 0.0417568 1228.139247 204.6898745 2590.875 C ficients Standard Error 18.34780437 0.015125962 Lower 95% 9.183522243 1.997904931 0.092695026 -4.12346504 40.819073810.5129608147.20856955 0.0058622642.580225395 0.0417568 0.000781519 0.02947041 -0.003297189 0.033549114 P-value 95% Lower 98.0% t Stat Upper Upper 98.0 Intercept X Variable 1

d) the model created cannot be used for prediction because 3635 is greater than the value of X used to formulate the model