Question

1. The correlation coefficient is

1. a unitless measure of the strength of the linear relationship between two quantitative variables
2. a unitless measure of the strength of the linear relationship between two categorical variables
3. measured in the same units as the larger quantitative variable
4. measured in the same units as the smaller quantitative variable

2. A random sample of 15 weeks of sales (measured in $) and 15 weeks of advertising expenses (measured in $) was taken and the sample correlation coefficient was found to be r = 0.80.  Based on this sample correlation coefficient we could state

1. That the percentage of the variation in sales that is shared with the variation in advertising is about 80%.
2. That the percentage of the variation in sales that is shared with the variation in advertising is about 64%.
3. That the percentage of variation that is shared by the two variables cannot be determined from the information given.
4. That the percentage of variation that is shared between the two variables is 100% because the two variables are positively correlated.

3. A scatterplot of two variables is constructed.  “Stretching” the scatterplot horizontally or vertically would

1. Change the perceived slope but not the correlation.
2. Change the correlation but not the perceived slope
3. Leave the correlation and the perceived slope unchanged.
4. Change both the correlation and the perceived slope.

4. A random sample of 40 students commuting to campus by bicycle is taken.  The correlation between the time spent waiting at traffic lights and total cycling time was r = 0.6.  This means:

1. The average rider spent sixty percent of their total cycling time to campus waiting at traffic lights.
2. The more time a rider spends waiting at traffic lights, the higher their total time commuting time is likely to be.
3. If the rider's time at traffic lights increases by 6 minutes, then they will spend an additional 12 minutes commuting to campus by bicycle, on the average.
4. If the rider's time at traffic lights increases by 12 minutes, then they will spend an additional 6 minutes commuting by bicycle, on the average.

Answer 1

The correlation coefficient is

a) unitless measure of the strength of the linear relationship between two quantitative variables

A random sample of 15 weeks of sales (measured in $) and 15 weeks of advertising expenses (measured in $) was taken and the sample correlation coefficient was found to be r = 0.80.  Based on this sample correlation coefficient we could state

c) That the percentage of variation that is shared by the two variables cannot be determined from the information given.( becauseb we use rsquare to determine variation not r)

A scatterplot of two variables is constructed.  “Stretching” the scatterplot horizontally or vertically would

a) Change the perceived slope but not the correlation.

A random sample of 40 students commuting to campus by bicycle is taken.  The correlation between the time spent waiting at traffic lights and total cycling time was r = 0.6.  This means:

b)The more time a rider spends waiting at traffic lights, the higher their total time commuting time is likely to be.