Question

In: Statistics and Probability

3.   You work for Segway, in the sales division of the One S1(which is basically a motorized...

3.   You work for Segway, in the sales division of the One S1(which is basically a motorized unicycle without the seat). You’ve collected data on monthly sales (S) and the price of the One S1 (P), both in dollars, as well as the daily average summer temperature in your most popular market (T) in degrees Fahrenheit. You estimate the following regression model: S = a + bP + cT. In your regressions, you usually look for a 10%-or-better level of confidence.

a.   What signs do you expect for a, b, and c?

b.   Your regression yields the following results:

Adjusted R Square

0.759

Independent Variables

Coefficients

Standard Error

t Stat

P-value

Intercept

62741

7912

7.930

0.00051

P

-49.79

10.22

-4.872

0.00459

T

-32.84

58.60

-0.561

0.59931

      Interpret what these coefficients mean.

c.   Does price have a statistically significant effect on sales?

d.   Does average temperature have a statistically significant effect on sales?

e.   What portion of the total variation in sales remains unexplained?

f.    Segway is considering selling the One S1 in a new city, where the average daily summer temperature is 75°, for a price of $580. What level of sales would you expect in this new city (rounded to the nearest dollar)?

Solutions

Expert Solution

a.       Expected sign of a is positive.

Expected Sign of b is negative. As the lower the price higher will be the sale.

Expected sign of c is negative. As lower the temprature higher will be the sale.

b.      The intercept a = 62741 is interpreted as we would expect average value of sale is $62741 if price (P) and temprature (T) are zero.

The coefficient b = -49.79 is interpreted as for every $1 increase in the price the average value of sale will decrease by $49.79 while temprature remains constant.

The coefficient c = -32.84 is interpreted as for every one degree increase in temperature the average value of the sale will decreased by $32.84 while price remains constant.

c.       Since the P value for price is 0.00459 is less than ? = 0.10 we reject null hypothesis. We can conclude that the price variable have statistically significant effect on sales.

d.      Since the P value for temprature is 0.0.59931 is greater than ? = 0.10 we can’t reject null hypothesis. We can conclude that the temprature variable have not statistically significant effect on sales.

e.      Unexplained variation = 1-0.759 = 0.241

The total variation in sales remains unexplained is 24.1%

f.        If temprature is 75o and price is $580 then the predicted value of sale is

62741 - 49.79*580 - 32.84*75 = 31399.8

The level of sales would you expect in this new city is 31399.8.

orchestra answered 2 years ago
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