Question

Can you solve it very urgently?

2. Suppose that Fashion Shoes sells another type of product, called “Infinity”, whose sales price changes frequently over time. The following table shows the total monthly sales of Infinity at each price level.

sale	price ($)
120	100
200	85
150	95
220	82
320	70
400	60
250	80
280	78
350	65
300	67
180	90
380	63

Run a simple linear regression on Excel and answer the following questions:

a) What is the coefficient of determination in this regression model? What does it tell us about the strength of the relationship between price and sales values of Infinity?

b) Is this regression significant? Check this claim at a 99% significance level by using an F-test. Confirm by observing the p-values.

c) What is the linear equation that shows the relationship between sales and price values of Infinity? Estimate the amount of sales for a price of $75.

d) What is the standard error of the estimate for this regression? Is it small or large compared to the estimated sales figures? Interpret.

Answer 1

1)

The coefficient of determination is 97%. It means around 97% of the variation is explained by the independent variable. Correlation measures the strength of association between two variables. Correlation tells how strongly two variables are associated with each other. The correlation between the price and sales values of Infinity is 0.98.

2)

Since the p-value of the regression coefficient is less than 0.05. Therefore, the regression is significant. if the calculated F value in a test is larger than F-statistic, Then we can reject the null hypothesis.

Therefore, F-Value(328.67) is greater than F-Statistics. So, reject the null hypothesis. All of the regression coefficients are not equal to zero.

3)

The linear regression line can be defined as:

The predicted amount of sales for the price of $75

Therefore, the estimated amount of sales for the price of $75 is 283.08