The following plot shows data taken from an experiment measuring the relationshi
ID: 3294664 • Letter: T
Question
The following plot shows data taken from an experiment measuring the relationship between speed and stopping distances of a car. The data had the following sample properties:
*Need help with calculating sloe, intercept of the regression line, regression equation, etc.
3) The following plot shows data taken from an experiment measuring the relationship between speed and stopping distances of a car. The data had the following sample properties: Vehicle Stopping Distances Mean Speed 15.4 mph SD Speed-5.29 mph Mean Stopping Dist 42.98 ft SD Stopping Dist-25.77 ft Correlation 0.81 10 15 20 25 3.a) Which variable is the explanato 3.b) Calculate the slope of the regression line. 3.c) How would you explain what the value of the slope means to someone who doesn't understand regression? 3.d) Calculate the intercept of the regression line. Does this value make sense in the context of the problem? 3.e) State the entire regression equation 3.f) For a vehicle traveling 18 miles an hour, how long do you think it would take to stop?Explanation / Answer
3. a) A variable used to predict or explain the values of the response variable is called explanatory variable. The explanatory variable is the one which is put on the x axis. The explanatory variable is speed.
b) The slope of th eregression line, beta1 is as follows:
beta1=r (Sdy/Sdx), where, Sdx is standard deviation of x and Sdy is standard deviation of y, r is correlation coefficient. Substitute the given values in the formula.
beta1=0.81(25.77/5.29)=3.946
c) With every 1 mph increase in speed, the stopping distance of a car is supposed to increase by 3.946 ft.
d) The y intercept, beta0=ybar-beta1 xbar=42.98-3.946(15.4)=-17.7884. Thi simplies that with 0 speed, the stopping distance of a car is -17.7884 ft. This does not make sense as stopping distance cannot be negative.
e) Substitute the values of slope and y intercept in th eregression equation to obtain the regression line.
yhat=-17.7884+3.946x
f) Substitute x with 18 to predict the stopping distance.
Stopping distance=-17.7884+3.946(18)=53.2396 ft
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