Case Study: ANALYSIS

ANALYSIS:

Using the table below, select the city that you will analyze based on the second letter of your last name.

Second Letter of Last Name Cities
a – f Dallas
g – n Chicago
o – z Denver

For example, since the 2nd letter in my last name, Steiner, is a t, I would analyze Denver.  However, Amy Adams, who’s 2nd letter in her last name is d, would analyze Dallas.

For your selected city, complete the following steps:

  • Create a simple scatterplot (without the regression line). Use Price as the predictor (x) variable and Volume as the response (y) variable.  Copy/ paste the scatterplot below.  Discuss if the linearity condition is satisfied. Also discuss the direction and strength of the association and any other observations you may have made.

The above scatter plot shows a linear relationship between price and volume. Therefore, the linearity condition is satisfied. The slope of the scatter points show a negative correlation between the two variables. The correlation between the variables may be weak because the data points are widely scattered with probable outliers.

  • Calculate the correlation coefficient, r, for Volume and Price. Copy/paste the Minitab results below.  Based on the correlation value, what do you conclude about the strength of the linear correlation between the Volume and Price of the frozen pizzas in this city?  Explain your answer.

Pearson correlation of Volume and Price = -0.531

P-Value = 0.000

The above results show that the correlation between volume and price is negative. The correlation coefficient is -0.531. This shows that price and volume have a medium correlation.

  • Find the value of R2 (using Minitab) between the Volume and Price. Explain what R2 means in this context.

R2  =  0.2820

The coefficient of determination is 0.2820. This implies that 28.20% of the variation in volume is attributed to the price.

  • Using Minitab, find the linear regression equation for Volume and Price for this city. Copy/paste the equation below.  Explain what the coefficient (slope) means in this context.

Regression Equation

Volume = 139547 – 33527 Price

The slope of the equaltion is -33527. This implies that when the price increases by one dollar, the volume decreases by 33,527.

  • Perform a hypothesis test to determine if the linear relationship between Volume and Price is significant. State your hypothesis and give the t-statistic and P-value (found using Minitab).  Based on the P-value, do you reject or fail to reject H0?  (Use a significance level of 0.05.) What does this mean for your final conclusion about the linear relationship?

Null hypothesis: There is no significant relationship between volume and price.

Alternative hypothesis: There is a significant relationship between volume and price.

The correlation between volume and price is significant because the p-value, 0.000 is less than the significance level, 0.05. Therefore, we reject the null hypothesis and conclude that the relationship between volume and price is significant.

  • Using your regression equation from Step 4, predict the volume when the price of the pizza is $2.50. Show your work below.  (Round to the nearest whole number.)

We substitute the value of $2.50 to the price.

Volume = 139547 – 33527(2.50) = 139547 – 83817.5 = 55,729.5 or 55,730

  • Using Minitab, find a 95% confidence interval for the mean volume for frozen pizza prices of $2.50 and find a 95% prediction interval for the volume when a frozen pizza is priced at $2.50. Copy/paste the Minitab results below.

Regression Equation

Volume = 139547 – 33527 Price

Variable  Setting

Price         2.5

Fit   SE Fit        95% CI              95% PI

55729.5  843.500  (54063.1, 57395.8)  (39121.0, 72338.0)