1. Consider the table that shows the driving experience in years (x) and the rating of driver (y). a) Complete the table. X x² xy y 0 1.2 1 2.1 2 3.6 3 4.2 4 5.6 5 6.8 6 8.4 $\sum$ $\sum$ y xy $\sum x^2$ $\sum y^2$ b) Find the equation of the line of the best fit manually. Show all your work. c) Calculate the coefficient of determination. d) Based on the coefficient of determination in question c) determine the correlation coefficient and interpret what it means about the correlation.
Added by Elizabeth R.
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First, let's calculate the mean of x and y: Mean of x = (0 + 1 + 2 + 3 + 4 + 5 + 6) / 7 = 3 Mean of y = (1.2 + 2.1 + 3.6 + 4.2 + 5.6 + 6.8 + 8.4) / 7 = 4.7 Show more…
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You wish to determine if there linear correlation between the age of a driver and the number of driver deaths. The following table represents the age of a driver and the number of driver deaths per 100,000. Use a significance level of 0.05 and round all values to 4 decimal places. Driver Age Number of Driver Deaths per 100,000 50 36 50 29 75 30 69 20 62 24 79 26 77 24 29 32 Ho: ρ = 0 Ha: ρ ≠ 0 Find the Linear Correlation Coefficient r =
Adi S.
Age Number of Driver Deaths per 100,000 16-19 38 20-24 36 25-34 24 35-54 20 55-74 18 75+ 28 a. For each age group, pick the midpoint of the interval for the x value. (For the 75+ group, use 80.) b. Using "ages" as the independent variable and "Number of driver deaths per 100,000" as the dependent variable, make a scatter plot of the data. (5 pts.) c. Calculate the least squares (best-fit) line. Put the equation in the form of: ŷ = a + bx d. Find the correlation coefficient. Is it significant? (5 pts.) e. Predict the number of deaths for ages 40 and 60. (5 pts.) f. Based on the given data, is there a linear relationship between age of a driver and driver fatality rate? (5 pts.) g. What is the slope of the least squares (best-fit) line? Interpret the slope. (5 pts.)
Jon S.
The value of a car is explained by a linear relationship with the age of the car. The correlation coefficient, r, is 0.397. About 16% of the variation in the value of the car is explained by a linear relationship with the age of the car. The coefficient of determination was r=0.158. When researchers looked at the association of x and y, they found that about 84% of the variation in the value of a car, y, is explained by a linear relationship with the age of the car, x.
Sri K.
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