Question

please quickly

Problem 1. Research performed at NASA measured the lengths of the right humerus and right tibia in eleven rats that were sent to space on Spacelab Life Sciences 2. The following data were collected. We will let length of the right humerus be the explanatory variable and the length of the right tibia be the response variable. Right Humerus (mm) 24.80 24.59 24.59 24.29 23.81 24.87 25.90 26.11 26.63 26.31 26.84 Right Tibia (mm) 36.05 35.57 35.57 34.58 34.20 34.73 37.38 37.96 37,46 37.75 38.50 (a) (2 points) Use Stat Crunch to make a scatter diagram of the data. Draw a rough sketch of the scatter diagram. (b) (2 points) Find the correlation coefficient between the two variables. Does a linear relation exist between them? (C) (2 points) Use StatCrunch to make a residual plot of the data. Draw a rough sketch of the residual plot. (d) (2 points) Will the least-squares regression line be a good model for the data? Why? (e) (2 points) Find the equation of the least squares regression line. (1) (2 points) Interpret the slope and y-intercept. (9) (2 points) One of the rats has a right humerus that is 26.11 mm and a right tibia that is 37.96 mm. Determine if the length of this tibia is above or below average.

Answer 1

(a)

Right Tibia y= 1.3902x + 1.114. 34 33.5 23.5 24 24.5 25 25.5 26 26.5 27

(b)

Therefore, R squared = 0.905002

Correlation Coefficient = n(Exy)-(Ex)(Ey) V[nɛx²-(Ex) [Ey?- (Ey)] na 11 se = 1 Exi = 278.74 = 25.34 ý = 1 Ey; = 399.75 = 36.34091 SSxx = Ex - I (Ex;)² = 100842399 SS yy = {y, ² - 1 (Ey;) 2 = 23.1532909 Ssxy = Exigi - 1 (Exi) Ey;) = 15.0728 SSXY 28 2.394 X 23.15 32909 = 0.951316

And a linear relation exists between them.

(c)

Right Humerus Residual Plot Residuals 24 25 26 27 Right Humerus

(d)

SUMMARY OUTPUT Regression Statistics Multiple R 0.951316 R Square 0.905002 Adjusted R 0.894447 Standard E 0.494358 Observatic 11 ANOVA df Regressior Residual Total SS MS F 1 20.95378 20.95378 85.73921 92.199508 0.24439 10 23.15329 Coefficientsandard Errit Stat P-value Intercept 1.113953 3.807312 0.292582 0.776474 Right Hum 1.390172 0.150134 9.259547 6.76E-06 RESIDUAL OUTPUT Observatiorcted Right Residuals 1 35.59022 0.459784 2 35.29828 0.27172 3 35.29828 0.27172 4 34.88123 -0.30123 5 34.21395 -0.01395 6 35.68753 -0.95753 7 37.11941 0.260595 8 37.41134 0.548659 9 38.13423 -0.67423 10 37.68938 0.060624 11 38.42617 0.073833

Since R Squared value is close to 1 and the P-value for Right Humerus's coefficient is very less we can say that least square regression line is good fit for the model.

(e)

is the equation of the least square regression line.

y = 1.3902x + 1.114

(f)The average Right tibia value for no right humerus is 1.114mm.

If the length of the Right humerus increases by 1mm then the length of Right tibia will increase by 1.3902.

(g) For x = 26.11 corresponding y = 37.412122. Average length of Right tibia is 37.412122 mm.

Therefore the length of this tibia is above average.