Question

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years.

                                                (Y)                                          (X)        

Sales in millions                     Advertising in ($10,000)

                                                15                                            32

                                                16                                            33

                                                18                                            35

                                                17                                            34

                                                16                                            36

(a) Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising.

(b) Use the method of least squares to compute an estimated regression line between sales and advertising by computing b0 and b1.

(c) If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars.

(d) What does the slope of the estimated regression line indicate?

(e) Compute the coefficient of determination for the estimated regression equation you got in the previous in-class problem.

(f) Interpret the meaning of the value of the coefficient of determination that you found in d. Be very specific.

(g) Perform a t test and determine whether or not X and Y are related. Let it = 0.05.

(h) Perform an F test and determine whether or not X and Y are related. Let it = 0.05.

Answer 1

a) The Scatter plot is given below---

it shows that as advertising increases sales also increases .

b) I have excel to fit a regression line----

Steps are---

enter the data and open data analysis tab---enter the information

the screen looks like----

The output of regression is-----

Fitted regression line is----

c)The predicted sales is---

i.e 18.8 million

d) slope=0.4 this is the average change in y if there is a unit change in value of x.

e) from regression output----

Coefficient of determination = 0.30

f) Coefficient of determination = 0.30, means 30% variation in y is explained by x.

g) from regression output---

t=1.1547 and p-value=0.33>0.05 so we accept the null hypothesis, I,e there is no relation between x and y.

h) from regression output---

F=1.33 and p-value=0.33>0.05 so we accept the null hypothesis, I,e there is no relation between x and y.