Question

Answer the following questions.

How related are triple hop and vertical jump performance in soccer players? The data below are distances (in cm) for these two tests from a random sample of 20 collegiate soccer players. (30 pts-7/3/3/3/5/7/2) Obs 6 Obs 1 2 3 Top Hop 781 601.67 479.34 447.53 553.23 Vert Jmp 71.1 57.6 43.68 42.05 37.66 7 8 9 Trpl Hop 467.6 4 77.62 4 83.32 6 67.12 644.69 Vert Jmp 49.97 42.57 37.59 61.5 59.38 Obs 11 12 13 14 15 Tepl Hop Vert Jmp 3 83 33 4 75.63 41.84 624.52 61.33 562.83 53.82 400.3148.42 Obs 16 17 18 1 9 20 Trpl Hop 568.04 465.88 683.56 464.71 686.42 Vert Jmp 47.53 34.14 48.55 35.76 65.85 10 The following table provides Excel output for the regression of vertical jump on triple hop. SUMMARY OUTPUT Regression Statistics Multiple R 0.82823988 0.6859813 R Square Adjusted R Square 0.66853582 Standard Error 5.42611733 Observations ANOVA F Significance F 6.5049E-06 1 MS 1623.77771 41.2949839 Regression Residual 39.3214273 55 1623.77771 743.30971 2 367.08742 19 Intercept Coefficients 2.08698306 0.08532686 Standard Error 7.56592786 0.01360727 Stat 0.27583967 .27067997 value 0.78581908 6.5049E- Lower 95% 13.808442 0.05672904 Upper 95% 1 7.9824077 0.11391463 Triple Hop 6 A scatterplot with regression line is below: VERTICAL JUMP (cm) 0 100 700 800 200 300 400 500 600 TRIPLE HOP (cm)

Answer 1

Ginem n=20 X = TRIPLE HOLE (com) YE VERTICAL jump (cm) girem n = 54529 cm Sx = 108.3cm T =.48.7cm Sy = 11.2cm s mg = 0.828 . i r Sre Sus - Sy 0,62811,2 . S2 > Sx 108.3 Bi = 0.08562) — the slope 80 = 9-8, X = 4827- 0.08562 (545.9) = 48.7 46.7 · T Be = 109557 equation of fitted line Yi = Rot Bixe Yi=10955 +0.0856 Xp ] 2) - S = (-4s + 0, 08s s x 4 574 Tû ĝo = 41.98156] a un acier / og li= Yi-ýi a df9/972 (84s8+000856724998! ei = 49.97. – 46.98156 Te = 9.98844)

R² = proposona of variability in vertical jump. explained by variability in hiple hop. R = 72 = (0.828)2 .. . R² = 0.6855 - 68.5584 5) indivi'lead prediction, for x = 500 cm 4 = -5 + 0.0% 6 x 500 Tŷ = 44.755 cm , SSE = Sing - Bo? Sy? = 11112) – (0.08 56)? (108.3)? = 125.44 – 85.941799 1SSE = 39.4982) MSE ES 3964982 20-2 = 2:1943 n-2 Confidence interval a 95% confidence interval for incluichead ( 4o + Tase ( it that (1985') x ternama T22918 = 2.1009, cest 2 30.05. ( 44.155 + 2.1948(1 + 1 + (500- Sus.m32J x 2.1009) (44.755 I 1.10887X20100g) (44.755 I 2-3296) → (42_4253 , 47.0846) Cami TM Own