A soft drink distributor was interested in examining the relationship between the number of ads (x) for his product during prime time on a local television station and the number of sales per week (y) in 1000’s of cases. He compiled the figures for 20 weeks and computed the following summary information: n=20, sum of x=92, sum of y=177, sum product of x and y=884, stdev of x=1.3917 and stdev of y=2.9069. Find the correlation coefficient for the number of ads during prime time

weekly sales.

There are several variations of the correlation coefficient formula. Find the one that will use the data given in your problem, then calculate r.

.9081

To find the correlation coefficient for the number of ads during prime time and weekly sales, we can use the formula for the correlation coefficient (r):

r = (sum of (x * y) - (sum of x * sum of y) / n) / (standard deviation of x * standard deviation of y)

Given the following values:

n = 20
sum of x = 92
sum of y = 177
sum of (x * y) = 884
standard deviation of x = 1.3917
standard deviation of y = 2.9069

We can now calculate the correlation coefficient:

r = (884 - (92 * 177 / 20)) / (1.3917 * 2.9069)
r = (884 - 911.4) / (4.0456)
r = -27.4 / 4.0456
r = -6.77

Therefore, the correlation coefficient for the number of ads during prime time and weekly sales is -6.77.

To find the correlation coefficient, also known as the Pearson correlation coefficient, we need to calculate several components using the given information:

1. Calculate the means of x and y:
mean_x = sum of x / n
mean_y = sum of y / n

In this case:
mean_x = 92 / 20 = 4.6
mean_y = 177 / 20 = 8.85

2. Calculate the deviations from the means for x and y:
deviation_x = x - mean_x
deviation_y = y - mean_y

For each observation (x, y), subtract the mean values obtained in step 1. For example, for the first observation:
deviation_x1 = x1 - mean_x = x1 - 4.6
deviation_y1 = y1 - mean_y = y1 - 8.85

Repeat this step for all observations.

3. Calculate the sum of the products of the deviations:
sum_product_deviations = sum of (deviation_x * deviation_y)

For each observation, multiply the corresponding deviations obtained in step 2 and sum the results:
sum_product_deviations = deviation_x1 * deviation_y1 + deviation_x2 * deviation_y2 + ... + deviation_x20 * deviation_y20
sum_product_deviations = sum of (x - mean_x) * (y - mean_y) = 884

4. Calculate the product of the standard deviations of x and y:
product_stddev = stddev_x * stddev_y

product_stddev = 1.3917 * 2.9069

5. Calculate the correlation coefficient:
correlation_coefficient = sum_product_deviations / (n * product_stddev)

Using the values obtained in the previous steps:
correlation_coefficient = 884 / (20 * (1.3917 * 2.9069))

Calculate this expression to find the correlation coefficient.

By following these steps, the correlation coefficient for the number of ads during prime time and weekly sales can be determined.