1. In a study on speed and braking distance, researchers looked for a method to estimate how fast a person was travelling before an accident by measuring the length of the skid marks. An area that was focused in the study, was how a vehicle at rations speeds may influence the distance required to complete' stop the vehicle. Below are the scatter plot and the regression results for the sample:
Summary Output-
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Regression Statistics
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Multiple R
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0,96579246
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R Square
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0,93275508
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Adjusted R Square
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0.915944
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Standard Error
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41.83697
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Observations
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6
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Coefficients
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Standard Error
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e Seat
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P-value
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Intercept
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-151.9
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43.87898537
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-3.46179
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0.025776
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Speed (in mph)
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6.45142857
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0.866107584
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7.448761
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0.001735
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a. What are the dependent variable (y) and the independent variable (x) in the regression model above?
b. State the estimated linear regression equation.
c. State and interpret the slope coefficient, b1 which depicts the changes in the braking distance by the vehicle speed.
d. Based on the scatter plot above, describe the relationship between the braking distance and the speed of the vehicles.
e. What is the coefficient of determination for the regression model? Interpret the value.
f. At 5% significance level, does the independent variable provide a significant contribution to the model? Discuss the result.
g. Predict the braking distance (in feet) when the speeds are 45mph and 100mph respectively. Are both predictions reliable?
2. At a customer's service counter, customers arrive at an average of 1.6 per minute. Calculate the probabilities that
a. At most 4 will arrive in any given minute.
b. At least 3 will arrive during an interval of 2 minutes.
c. How many customers are expected to arrive in 5 minutes?