A study performed in 1984 examined the relationship between the price of gasoline in Great Britain and the distance driven by motorists. For a random sample of 15 months, the average price of gasoline was recorded ("Gas") as well as the total number of kilometers driven that month ("Drive"). This data is shown in the two vectors below. Drive=c(15220,15552,19205,16551,13885,20997,16909,19453,16758,16224,18308,15226,11196,13842,11823); Gas=c(0.0928,0.1152,0.118,0.117,0.0887,0.1201,0.1091,0.1245,0.1087,0.1178,0.1131,0.1048,0.0845,0.0893,0.101); a. Find the correlation between the price of gasoline and the total number of kilometers driven. _______________ Round to at least five decimals if necessary b. State the regression equation that expresses the total number of kilometers driven (Y) as a linear function of the price of gasoline (X). Give all decimals. Yi = _________ +/- _________ Xi c. Which is the correct interpretation of β1 in the above regression equation? As the price of gasoline increases by $ 1, the total number of kilometers driven increases on average by β1 km The price of gasoline for a month where the total number of kilometers driven is 0 km is, on average, $ β1 As the price of gasoline increases by $ β1, the total number of kilometers driven increases on average by 1 km As the price of gasoline increases by $ 1, the total number of kilometers driven increases by β1 km As the price of gasoline increases by $ β1, the total number of kilometers driven increases by 1 km The total number of kilometers driven for a month where the gasoline price is $ 0 is, on average, β1
A study performed in 1984 examined the relationship between the price of gasoline in Great Britain and the distance driven by motorists. For a random sample of 15 months, the average price of gasoline was recorded ("Gas") as well as the total number of kilometers driven that month ("Drive"). This data is shown in the two vectors below.
Drive=c(15220,15552,19205,16551,13885,20997,16909,19453,16758,16224,18308,15226,11196,13842,11823);
Gas=c(0.0928,0.1152,0.118,0.117,0.0887,0.1201,0.1091,0.1245,0.1087,0.1178,0.1131,0.1048,0.0845,0.0893,0.101);
a. Find the
_______________ Round to at least five decimals if necessary
b. State the regression equation that expresses the total number of kilometers driven (Y) as a linear
Yi = _________ +/- _________ Xi
c. Which is the correct interpretation of β1 in the above regression equation?
- As the price of gasoline increases by $ 1, the total number of kilometers driven increases on average by β1 km
- The price of gasoline for a month where the total number of kilometers driven is 0 km is, on average, $ β1
- As the price of gasoline increases by $ β1, the total number of kilometers driven increases on average by 1 km
- As the price of gasoline increases by $ 1, the total number of kilometers driven increases by β1 km
- As the price of gasoline increases by $ β1, the total number of kilometers driven increases by 1 km
- The total number of kilometers driven for a month where the gasoline price is $ 0 is, on average, β1
d. The coefficient of determination tells us that _______% of the variation in the:
A. price of gasoline
B. total number of kilometers driven
is explained by its linear relationship with the:
A. price of gasoline
B. total number of kilometers driven
e. The sixth month in the dataset is a month in which gasoline cost $ 0.1201 and a total of 20997 kilometers were driven. Compute the residual for this month.
e = ______ Round to five decimals if necessary
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