Question

I‘m not sure about this question, please show your work thanks!

For question 1 in this assignment we will investigate data collected by a student to try to infer a person's stature from their footprints, for forensic purposes. The goal would be to identify the stature of an unseen suspect from evidence (such as a foot print) left at a crime scene. (Rohren, B. 2006. Estimation of Stature from Foot and Shoe Length: Applications in Forensic Science, obtained from Triola Elementary Statistics.) The variables in the data set are the length of shoe measured from a shoe print left (cm), and individual height (cm) Question 1. If these data are to be used for forensic purposes, to estimate a characteristic of a suspect based on evidence they leave on the scene; a) Which is the explanatory variable and which is the response variable? b) Which of these scatterplots correctly display the data? Explain why i) 26 28 30 32 34 160 170 180 190 Shoe print length (cm) Height (cm) b) Given the scatterplot, explain whether you think a linear model is reasonable for these data c) Which of these is the most likely value for the correlation coefficient between these two variables? Explain i) 0.25 d) The following are the coefficients for the linear model estimated for these data bo 80.9; b1 3.2 Given this model, predict a person's height for the following shoe print lengths. If you think it is inappropriate )-0.25 iii) 0.8 iv) -0.8 V) 0.99 vi) -0.99 to make a prediction, explain why i) 15 cm i) 27 cm ii) 31 cm

Answer 1

a) In this data, the student is trying to infer a person's stature from their footprints, for forensic purposes. Therefore it is the shoe print length(footprint) which is the explanatory variable and the height is the response variable.

b) It is general convention to plot the explanatory variable along the X-axis of the scatterplot and to plot the response variable along the Y-axis of the scatterplot. Therefore in this case scatterplot i) correctly displays the data.

b) Given the scatterplot, a linear model would be reasonable for the data because the scatterplot shows a somewhat linear increment  in the X and Y variable values. Given that the shoe print length of an individual from the data increases , the height of the person also seems to increase

c) Out of the following values the most likely value for the correlation coefficient between these two variables is 0.8. The values of Y are increasing along with the values of X. So it is clear that there is positive correlation between the two variables. Now it is also quite clear that there exists a high correlation between the two variables since Y tends to linearly increase with X. But it is not absolutely along a single straight line , so 0.99 would be an overestimation.

d) If b₀ = 80.9 and b₁ = 3.2 then

The linear model is as follows

Y = 80.9 + 3.2X

i) For X(Shoe print length) = 15cm

Y= 80.9 + 3.2 * 15

Y(height)=  128.9 cm

ii) X=27cm

Y= 80.9 + 3.2*27

Y= 167.3 cm

iii) X=31cm

Y= 80.9 + 3.2 * 31

Y=180.1cm

It is appropriate to make a prediction since the correlation coefficient is high in the data. Which means that coefficient of determination (R²) will also be more or less high.