Answer to Question #262912 in Statistics and Probability for Zumuto

Question

Online Store Monthly E- Commerce sales (in 1000s)Online Advertising (1000s)13681.7023401.5036652.8049545.0053311.3065562.2073761.30

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c} Online & Monthly\ E- & Online\ Advertising \\ Store & commerse\ Sales & Dollars \\ & \ (in\ 1000s) & (1000s)\\ \hline 1 & 368 & 1.7\\ 2 & 340 & 1.5\\ 3 & 665 & 2.8\\ 4 & 954 & 5\\ 5 & 331 & 1.3\\ 6 & 556 & 2.2\\ 7 & 376 & 1.3\\ \end{array}$$

a) Online Advertising Dollars is independent variable $(X).$

Monthly E-commerse Sales is dependent variable $(Y).$

$$\bar{X}=\dfrac{1}{n}\sum_iX_i=\dfrac{15.8}{7}=2.257143$$

$$\bar{Y}=\dfrac{1}{n}\sum_iY_i=\dfrac{3590}{7}=512.857143$$

$$SS_{XX}=\sum_i(X_i-\bar{X})^2=10.537143$$

$$SS_{YY}=\sum_i(Y_i-\bar{Y})^2=322280.857143$$

$$SS_{XY}=\sum_i(X_i-\bar{X})(Y_i-\bar{Y})=1806.757143$$

$$m=slope=\dfrac{SS_{XY}}{SS_{XX}}=\dfrac{1806.757143}{10.537143}=171.465564$$

$$n=\bar{Y}-m\bar{X}$$

$$=512.857143-171.465564(2.257143)$$

$$=125.834870$$

Therefore, we find that the regression equation is:

$$Y=125.834870+171.465564X$$

b) Correlation coefficient:

$$r=\dfrac{SS_{XY}}{\sqrt{SS_{XX}}\sqrt{SS_{YY}}}$$

$$=\dfrac{1806.757143}{\sqrt{10.537143}\sqrt{322280.857143}}$$

$$=0.980440$$

We have strong positive correlation.