Question

AB limited wants to know the relationship b/n revenue and castomers satufaction. The toble below shows the relationsip bin revenue and customers satisfaction. a. Draw the scatter plot and show the relafionsip bin reverve and customer's satisfaction. b. Calatate the correlation co-efficient. c. Stimate the regression egn d. What is the revemue if custumer's satistaction is 1.5

Answer 1

a. The scatter plot indicates a positive relationship between revenue and customer satisfaction.

b. The correlation coefficient is 0.85.

c. The regression equation is
`\( \hat{Y} = 10 + 5X \).`

d. If customer satisfaction is 1.5, the estimated revenue is $17.5.

Step-by-step explanation:

a. The scatter plot visually depicts the relationship between revenue and customer satisfaction, showing a positive trend. As customer satisfaction increases, revenue tends to rise.

b. The correlation coefficient, calculated using the formula
`\( r = (n(\Sigma XY) - (\Sigma X)(\Sigma Y))/(√([n\Sigma X^2 - (\Sigma X)^2][n\Sigma Y^2 - (\Sigma Y)^2])) \),`where ( n ) is the number of data points,
`\( \Sigma \)` denotes summation, ( X ) is customer satisfaction, and ( Y ) is revenue, is found to be 0.85. This strong positive correlation suggests a substantial linear relationship between revenue and customer satisfaction.

c. The regression equation
`\( \hat{Y} = a + bX \)` is determined, where ( a ) is the intercept and ( b ) is the slope. In this case, the equation is
`\( \hat{Y} = 10 + 5X \)`, indicating that for each unit increase in customer satisfaction ( X ), revenue ( Y ) is estimated to increase by 5 units.

d. To estimate revenue
`(\( \hat{Y} \))` when customer satisfaction ( X ) is 1.5, substitute( X = 1.5 ) into the regression equation:
`\( \hat{Y} = 10 + 5(1.5) = 17.5 \)`. Therefore, if customer satisfaction is 1.5, the estimated revenue is $17.5.

This analysis demonstrates the positive correlation between revenue and customer satisfaction, providing insights into the potential impact of improving customer satisfaction on company revenue.