Speed (mph) Stopping Distances (ft)20 64, 62, 5930 114, 118, 10540 153, 171, 16550 231, 203, 23860 317, 321, 276 Brakes The table below shows stopping distances in feetfor a car tested 3 times at each of 5 speeds. We hope tocreate a model that predicts Stopping Distance from theSpeed of the car.a) Explain why a linear model is not appropriate.b) Re-express the data to straighten the scatterplot.c) Create an appropriate model.d) Estimate the stopping distance for a car traveling 55 mph.e) Estimate the stopping distance for a car traveling 70 mph.f) How much confidence do you place in these predic-tions? Why?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Speed (mph) Stopping Distances (ft)
20 64, 62, 59
30 114, 118, 105
40 153, 171, 165
50 231, 203, 238
60 317, 321, 276
Brakes The table below shows stopping distances in feet
for a car tested 3 times at each of 5 speeds. We hope to
create a model that predicts Stopping Distance from the
Speed of the car.
a) Explain why a linear model is not appropriate.
b) Re-express the data to straighten the scatterplot.
c) Create an appropriate model.
d) Estimate the stopping distance for a car traveling 55 mph.
e) Estimate the stopping distance for a car traveling 70 mph.
f) How much confidence do you place in these predic-
tions? Why?
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