Question

In: Statistics and Probability

For 45 cities in the U.S, we found a correlation of 0.86 between internet use and...

For 45 cities in the U.S, we found a correlation of 0.86 between internet use and

online shopping. The regression equation predicting online shopping is ŷ =15+ 0.8 *Internet use

a. Based on the correlation value, is the slope positive or negative? Why?

b. Honolulu had an internet use of 91% and online shopping of 85%. Find its predicted online

shopping based on the regression equation.

c. Find the residual for Honolulu. Interpret the result

Expert Solution

Solution:

a) The slope of the regression equation is positive, because the value of the correlation coefficient between internet use and online shopping is 0.86. Means that as internet use increases then online shopping increases . There is strong positive correlation between internet use and online shopping.

b) The estimated regression equation for predicting online shopping is

When internet use of 91% then the observed or actual online shopping is y = 85%

To predict online shopping when internet use = 91% is

%

c) The residuals can be calculated as = observed value - estimated value

Residuals = 85 - 87.8

Residuals = -2.8%

Interpretation:

The residuals should be small and unstructured this means that the regression equation has been successful in explaining the variation of the dependent variable online shopping.

orchestra answered 1 year ago

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