week 5 _ discussion

AMBER WROTE:

Do you observe a relationship between both variables?

Yes there is a positive linear relationship between sales and advertisement.

Use Excel to fit a linear regression line to the data. What is the fitted regression model? (Hint: You can follow the steps outlined in Fitting a Regression on a Scatter Plot on page 497 of the textbook.)

The fitted regression model is sales = -25.1689 + 4.9216 advertisement.

What is the slope? What does the slope tell us?Is the slope significant?

The slope is 4.9216 for every one dollar spent on advertisement there is a corresponding 4.9216 increase in sales.

What is the intercept? Is it meaningful?

The intercept is 25.168 Here the intercept is negative. The negative intercept tells you where the linear model predicts sales(y) would be when advertisement (x) is 0. 

What is the value of the regression coefficient,r? What is the value of the coefficient of determination, r^2? What does r^2 tell us?

Regression coefficient,r=0.6785=0.824. The value of the coefficient of determination, R2=0.6785. Coefficient of determination tells us how well the regression model fits the observed data. Higher the coefficient, better fit is the model.

Use the model to predict sales and the business spends $950,000 in advertisement. Does the model underestimate or overestimates ales?

The model predicts sales and the business spends 950,000 in advertisement is sales = -25.1619 + 6.9216 x 950 = 460.3518 

GRACIE WROTE:

Hi class, 

After creating a scatterplot for the provided data, there is an obvious upward trend. This indicates a positive correlation between advertising costs and sales. As the amount of advertising costs increases, so does the amount of sales. The general formula of the regression equation is y= a + bx. In the equation "a" is the intercept and "b" is the slope. Using the data, the equation is noted as y=4.9216 x -25.168, and the slope (b) is 4.9216. The slope is the steepness of the line. Because the slope is not equal to zero, it is significant.

What is the value of the regression coefficient,r? What is the value of the coefficient of determination, r^2? What does r^2 tell us?

The value of the regression coefficient, “r” is 0.823733298 and “r2” is 0.6785. The coefficient of determination tells us how well the regression model fits the data. After converting the r2 value to a percentage, it shows a turnover variation of 67.85 percent. This shows that the model has a better fit.

Use the model to predict sales and the business spends $950,000 in the advertisement. Does the model underestimate or overestimate ales?

If the company spends $950,000 in advertising expenses, the projected revenue is $4,650,352. If the company reduces expenses to $938,000, the corresponding sales will be $5,506,000. This indicates that the regression model underestimates sales.