Math Statistics 4) Researchers continue to look for methods to measure how fast
ID: 3072973 • Letter: M
Question
Math Statistics
4) Researchers continue to look for methods to measure how fast a car was traveling before an accident. Most methods focus on the distance, d (in feet) required for an average car to completely stop while traveling at various speeds, s. Consider the table below MPH (s 2030 405060 80 Breaking Distance (d) 18 38 57 82126 243 a) Use your graphing calculator to find the linear model and correlation coefficient. Enter the data into L1 and L2, and then got to STAT- CALC- LinReg. Be sure that you have turned diagnostics on. (3 points) b) Use the model to predict the breaking distance for a car traveling 70 mph. (1 point) c) What is the observed breaking distance for a car traveling 40 mph? What is the predicted distance for a car traveling 40 mph? (2 points) d) Find the residual for a car traveling 40 mph and interpret its meaning. (2 points)Explanation / Answer
a )
Using TI-84
Steps :
STAT ---> edit ---> Enter data in L1 and L2 ( MPH in L1 and Breaking distance in L2 ) ----> Press STAT -----> CALC ---> Select : LinReg( ax + b ) -----> Xlist : L1 , Ylist : L2 ----> Highlight calculate and hit Enter.
Result :
Y = ax + b
a = 3.6686
b = -77.2
correlation coefficient = r = 0.9660
Linear model : y = 3.6686*x - 77.2
b )
we have to predict the beraking distance for a car traveling 70 Mph.
Linear model : y = 3.6686*x - 77.2
Plug x = 70
y = 3.6686*70 - 77.2
y =179.602
Predicted value for the beraking distance for a car traveling 70 Mph is 179.602
c )
Observed beraking distance for a car traveling 40 Mph = 57 ( using given data )
Predicted beraking distance for a car traveling 40 Mph is ,
y = 3.6686*40 - 77.2 ( Using linear model )
y = 69.544
d )
Residual = Observed value - Predicted value.
Observed beraking distance for a car traveling 40 Mph = 57
Predicted beraking distance for a car traveling 40 Mph = 69.544
So, Residual = 57 - 69.544 = - 12.544