1. Given the correlation coefficient -0.994 and the linear regression equation Å· = 212 - 1.81x, compute the coefficient of determination.
r^2 =
Round to 4 decimal places.
2. The birth lengths in cm (x) and birth weights in kg (y) of a sample of 50 newborn female babies are compared, yielding a correlation coefficient of r = 0.578 and a linear regression equation of Å· = -8.89 + 0.243x. The babies all had lengths between 46.5 and 53.0 cm, and weights between 2.50 and 4.05 kg.
Based on this, predict the birth weight of a newborn female baby with a birth length of 48.5 cm.
i. Is it appropriate to use the linear regression equation to make the requested prediction for the value of the unknown variable?
Yes No
ii. Compute the predicted birth weight.
(Input 0 if your answer to part (i) is no.)
kg
Round to two decimal places.
3. Complete the following instructions:
i. Identify the independent and dependent variables.
ii. Calculate and interpret the Pearson correlation coefficient (r) for the paired data. Be sure to indicate if the correlation is positive or negative, and whether it is strong, moderate, or weak, or if there does not appear to be any significant correlation.
An LCBO employee compares the relationship between the price of 6 different vintage bottles of wine, and the number of those bottles that have been purchased in the last 3 months to see if there is a correlation between the number of bottles purchased and the price of the bottle.
Number of Bottles of Wine Purchased in the Last 3 Months
Price of Wine Bottle ($)
44
25
18
60
93
15
65
30
82
20
56
40
i. Independent Variable:
Number of Bottles of Wine Purchased in the Last 3 Months Price of Wine Bottle ($)
Dependent Variable:
Number of Bottles of Wine Purchased in the Last 3 Months Price of Wine Bottle ($)
ii. Pearson Correlation Coefficient (r):
Round to 3 decimal places.
Correlation:
Positive Negative Neither
Correlation Strength:
Strong Moderate Weak No Significant Correlation
4. An online marketplace retailer performed a study that compared the average domestic shipping time of 93 sellers with their overall seller satisfaction rating (as a percent). The study yielded a sample correlation coefficient of r = -0.143. Test the claim that there is no linear correlation between the seller's average shipping time and their overall satisfaction rating at the 20% level of significance.
a. Calculate the test statistic.
t =
Round to three decimal places if necessary
b. Determine the critical value(s) for the hypothesis test.
c. Conclude whether to reject the null hypothesis or not based on the test statistic.
Reject
Fail to Reject