Question

Problem 1. Correlation. The U.S. government has been interested in pushing auto manufacturers to increase the MPG of their fleet. One goal set in 2006 was to have an average (combined city and highway) Miles Per Gallon (MPG) for SUV vehicles of 22 by 2011. A sample of 100 SUVs from 2018 and several variables were measured. The key variables are given below, along with basic Univariate statistics for each one: • MPGavg • MPGcity • MPGhwy • Eng Size • Cyl_4Dum • Cyl_6Dum • Cyl_8Dum A weighted average of miles per gallon, 60% highway and 40% city The estimated miles per gallon for city driving The estimated miles per gallon for city driving The size of the engine in liters A dummy variable coded as one if the engine is 4 cylinders, zero for 6 or 8 cylinder SUVs A dummy variable coded as one if the engine is 6 cylinders, zero for 4 or 8 cylinder SUVs A dummy variable coded as one if the engine is 8 cylinders, zero for 4 or 6 cylinder SUVs Univariate Simple Statistics Column N Mean MPGavg 100 21.2300 MPGcity 100 18.8400 MPGhwy 100 25.1000 Eng Size 100 3.2000 Cyl_4Dum 100 0.4500 Cyl_6Dum 100 0.3300 Cyl_8Dum 100 0.2200 Std Dev Sum Minimum Maximum 3.3751 2123.0000 14.0000 29.0000 3.2309 1884.0000 13.0000 26.0000 3.5434 2510.0000 17.0000 33.0000 1.2965 320.0000 1.4000 6.2000 0.5000 45.0000 0.0000 1.0000 0.4726 33.0000 0.0000 1.0000 0.4163 22.0000 0.0000 1.0000 Cyl_4Dum Cyl_6Dum Cyl_8Dum The Correlations Matrix is given below MPGavg MPGcity MPGhwy Eng Size MPGavg 1.0000 MPGcity 0.9844 1.0000 MPGhwy 0.9711 0.9349 1.0000 Eng Size -0.8437 -0.8592 -0.779 1.0000 Cyl_4Dum 0.8000 0.8079 0.7554 -0.7916 Cyl_6Dum -0.2507 -0.2495 -0.2431 0.1105 Cyl_8Dum -0.6762 -0.6869 -0.6313 0.8253 1.0000 -0.6348 -0.4804 1.0000 -0.3727 1.0000
Based on the information above, what proportion of the SUVs are 8 cylinder vehicles (I want the proportion and not the percentage)? I just want the numerical answer. Use 4 decimal places and use the proper rules of rounding. PLEASE SHOW WORK

Answer 1

From the column of Mean which is in the table with title Univariate simple statistics,

We can conclude that,

Out of 100 SUVs,

45 are with 4 cylinder, 33 are with 6 cylinder and 22 are with 8 cylinder.

Hence,

Proportion of SUVs with 8 cylinder is given by,

Proportion=22/100

Proportion=0.2200

Which is the required answer.

Thank you.