Calculate the deviations from the average, the manual correlation calculation and cross check it with Excel’s correl function
Deviations from the average
Directions:
For each problem, you must calculate the deviations from the average, the manual correlation calculation and cross check it with Excel’s correl function. Furthermore, you will generate the scatterplot graph, along with the trendline. Indicate whether there is a strong/weak/no correlation between the two variables.
PRACTICE QUESTION 1: deviations from the average
The Swiss Hiking Federation is an organization that is known for promoting the same use of the hiking trail system throughout Switzerland. Suppose SHF would like to investigate the linear relationship between the amount of time to hike Wengen-Kleine trail in the Jungfrau region and the age of the hiker. A random sample of 7 hikers on this trail was selected and their age and hiking time is below.
AGE:Â 24Â Â Â Â Â Â 32Â Â Â Â Â Â 47Â Â Â Â Â Â 40Â Â Â Â Â Â 26Â Â Â Â Â Â 53Â Â Â Â Â Â 38
TIME: 2.7Â Â Â Â Â 4.2Â Â Â Â Â 5.0Â Â Â Â Â 3.8Â Â Â Â Â 2.2Â Â Â Â Â 2.9Â Â Â Â Â 3.0
Using XLS, calculate the correlation coefficient for this sample. Test to see if the population correlation coefficient is not equal to zero using a 90% CI. Here, you will use a two-tail test.
PRACTICE QUESTION 2: deviations from the average
Consider the following
X:Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 7Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 6
Y:Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 9Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 7
Using XLS, calculate the correlation coefficient for this sample. Test to see if the population correlation coefficient is not equal to zero using significance of 0.05. What are your conclusions?
PRACTICE QUESTION 3:
Fair Isaac, the company that developed the credit score (FICO) model used by most lenders today, would like to test the linear relationship between age and credit score of an individual. The follow table shows the credit scores and ages of 10 randomly selected individuals:
AGE:Â 36Â Â Â Â Â Â 24Â Â Â Â Â Â 54Â Â Â Â Â Â 28 Â Â Â Â Â Â 31Â Â Â Â Â Â 47Â Â Â Â Â Â 35Â Â Â Â Â Â 59Â Â Â Â Â Â 40Â Â Â Â Â Â 42
FICO: 675Â Â Â Â 655Â Â Â Â 760Â Â Â Â 615Â Â Â Â 660Â Â Â Â 790Â Â Â Â 720Â Â Â Â 760Â Â Â Â 685Â Â Â Â 610
Using XLS, calculate the correlation coefficient for this sample. Test to see if the population correlation coefficient is different from zero, using an significance of 0.02. What are your conclusions?
PRACTICE QUESTION 4:
The following tables shows the selling prices, in thousands of dollars, and the square footages of seven randomly selected homes recently sold by Century 21 Realtors:
Price: Â 258Â Â Â Â 191Â Â Â Â 253Â Â Â Â 168Â Â Â Â 249Â Â Â Â 245Â Â Â Â 282
Sqr Ft:Â Â 2730Â Â Â Â Â Â Â Â Â Â Â Â 1860Â Â 2140Â Â 2180Â Â 2310Â Â 2450Â Â 2920
Using XLS, calculate the correlation coefficient for this sample. Using an significance of .1, test the significance of the population correlation coefficient between a house’s selling price and its square footage. What conclusions can you draw?
PRACTICE QUESTION 5: deviations from the average
The following tables shows the mpg and curbed weight, in thousands for eight randomly selected vehicles:
MPG:Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 28Â Â Â Â Â Â 22Â Â Â Â Â Â 20Â Â Â Â Â Â 34Â Â Â Â Â Â 41Â Â Â Â Â Â 15Â Â Â Â Â Â 19Â Â Â Â Â Â 15
Weight:Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2730Â Â 2860Â Â 3140Â Â 2180Â Â 2310Â Â 4450Â Â 3920Â Â 2590
Using XLS, calculate the correlation coefficient for this sample. Using an significance of .1, test the significance of the population correlation coefficient is negatively related between mpg and curbed weight. What conclusions can you draw?
