Question

(Minitab)

Ice Cream Sales

Answer the following questions, showing any calculations involved. Include this document along with the graphs created with Minitab in your submission.

1. Identify the independent (predictor) and dependent (response) variables. [2 pts]

Independent variable: __________________ Dependent variable: __________________

2. From the scatter diagram, does there seem to be a linear correlation? If so, is it strong or weak? Is it positive or negative? What does it say about the relationship between the 2 variables? [4 pts]

3. Use your scatter diagram to answer the following questions.
   1. If you calculated the linear correlation coefficient for this data to be r = –0.75, explain in one sentence how you know this is incorrect. [2 pts]
   2. If you calculated the linear correlation coefficient for this data to be r = 1.20, explain in one sentence how you know this is incorrect. [2 pts]

4. What is the correlation coefficient, r. Based on the correlation coefficient, how accurate do you think your regression equation is at making a prediction? Why? [2 pts]

5. What is the p-value? Is a linear relationship appropriate? How do you know? [2 pts]

6. Identify the following quantities: [3 pts]

Regression Equation: ______________________________

Slope: _______________ y-Intercept: _______________

7. Explain the meaning of the slope in terms of this problem. [5 pts]

8. Explain the meaning of the y-intercept in terms of this problem. Is it meaningful? Why or why not? [5 pts]

9. Predict the ice cream cone sales on a day where the high temperature was 75°.

10. On a 70° day, the Creamery had sales of 400 ice cream cones. Is this sales figure above or below the average for this temperature? Show your work for credit. [2 pts]

11. Answer the following questions.
    1. The high temperature on Saturday is predicted to be 75°. Would it be reasonable to use the regression equation you created to predict this day’s sales? Why or why not? [2 pts]
    2. The high temperature on Sunday is predicted to be 85°. Would it be reasonable to use the regression equation you created to predict this day’s sales? Why or why not? [2 pts]

1. 3. The high temperature on Sunday at the Creamery’s Buffalo store is predicted to be 74°. Would it be reasonable to use the regression equation you created to predict this store’s sales? Why or why not? [2 pts]

12. Compute and interpret R². [4 pts]

Ice Cream Data

Temperature F Sales

57.6        215

61.5        325

53.4        185

59.4        332

65.3        406

71.8        522

66.9        412

77.2        614

74.1        544

64.6        421

72.7        445

63.0        408

64.4        250

66.2        345

73.4        459

62.6        349

66.2        311

73.4        463

59.0        262

73.4        462

55.4        274

75.2        459

55.4        252

69.8        426

57.2        289

69.8        438

57.2        311

68.0        448

64.4        257

73.4        477

64.4        319

73.4        479

71.6        490

60.8        347

59.0        349

68.0        436

               

Answer 1

Identify the independent (predictor) and dependent (response) variables. [2 pts]
Independent variable: Temperature Dependent variable: Sales

From the scatter diagram, does there seem to be a linear correlation? If so, is it strong or weak? Is it positive or negative? What does it say about the relationship between the 2 variables? [4 pts]
Yes there is linear correlation. It a strong. It is positve. As the temperature increases, the sales also increases.

Use your scatter diagram to answer the following questions.
If you calculated the linear correlation coefficient for this data to be r = –0.75, explain in one sentence how you know this is incorrect. [2 pts]
It is incorrect since, intitutively the relationship between the two variables cannot be negative or inverse, that is as one increase, the other one decreases.

If you calculated the linear correlation coefficient for this data to be r = 1.20, explain in one sentence how you know this is incorrect. [2 pts]
It is incorrect, because the correlation can be more than 1.

What is the correlation coefficient, r. Based on the correlation coefficient, how accurate do you think your regression equation is at making a prediction?
Why? [2 pts]
The correlation is 0.88.
From the correlation we have can find the coefficient of determination = 0.94 ( it is the square root of the correlation).
It is the measure of the amount of variability in y explained by x. Its value lies between 0 and 1. Greater the value, better is the model. In this case, it 94%, hence the model is good