Discussion - 5

1.Using data set E, answer the questions given below.  

 Click here for the Excel Data File   Choose the dependent variable (the response variable to be "explained") and the independent variable (the predictor or explanatory variable).   Dependent Variable    multiple choice 1

· Power

· Speed

  Independent Variable    multiple choice 2

· Power

· Speed

  Obtain the regression equation. (Round your answers to 3 decimal places.)    Y =   X +     Calculate R2. (Round your answer to 3 decimal places.)   

2. Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodles & Company restaurants.

 Click here for the Excel Data File   (b) Find the correlation coefficient. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)    r               (c-1) To test the correlation coefficient for significance at α = 0.025, fill in the following. (Use the rounded value of the correlation coefficient from part b in all calculations. For final answers, round tcalc to 3 decimal places and the p-value to 4 decimal places. Negative values should be indicated by a minus sign.)

(c-2) There is no significant correlation.    multiple choice 1

· True

· False

  (d) Does it appear that increased loyalty card usage is associated with decreased sales growth?    multiple choice 2

· No

Yes

3. Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors’ advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit).  

  (a) Write the fitted regression equation. (Round your coefficient CompetingAds to 3 decimal places, coefficient Price to 4 decimal places, and other values to 2 decimal places. Negative values should be indicated by a minus sign.)   yˆy^ =  +  * FloorSpace +  * CompetingAds +  * Price   (b-1) The coefficient of FloorSpace says that each additional square foot of floor space   multiple choice 1

· takes away 12.48 from sales (in thousands of dollars).

· adds about 12.48 to sales (in thousands of dollars).

· takes away 0.1496 from sales (in thousands of dollars).

· adds about 6.915 to sales (in thousands of dollars).

  (b-2) The coefficient of CompetingAds says that each additional $1,000 of "competitors' advertising expenditures"   multiple choice 2

· takes away 0.1437 from sales (in thousands of dollars).

· takes away12.48 from sales (in thousands of dollars).

· reduces sales by about 6.915 from sales (in thousands of dollars).

· adds about 6.915 to sales (in thousands of dollars).

  (b-3) The coefficient of Price says that each additional $1 of advertised price   multiple choice 3

· adds about 6.915 to sales (in thousands of dollars).

· reduces sales by about 6.915 from sales (in thousands of dollars).

· takes away 12.48 from sales (in thousands of dollars).

· reduces sales by about 0.1437 from sales (in thousands of dollars).

  (c) The intercept is not meaningful, since a mountain bike cannot sell for zero, which will happen if all the variables are zero.   multiple choice 4

· True

· False

  (d) Make a prediction for Sales when FloorSpace = 93, CompetingAds = 97, and Price = 1,338. (Enter your answer in thousands. Round your answer to 2 decimal places.)   Sales           $  thousand

4. Simple regression was employed to establish the effects of childhood exposure to lead. The effective sample size was about 122 subjects. The independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.   (a) Calculate the t statistic for each slope. From the p-values, which slopes differ from zero at α = .01? (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)  

(b) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted. multiple choice 10

· No

Yes

5. A regression model to predict Y, the state-by-state 2005 burglary crime rate per 100,000 people, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies per 1,000 people, X3 = 2004 federal expenditures per capita, and X4 = 2005 high school graduation percentage.  

  (a) Write the fitted regression equation. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign.)   yˆy^ =  +  AgeMed +  Bankrupt +  FedSpend +   HSGrad%   (b-1) The 2005 state-by-state crime rate per 100,000   multiple choice 1

· increases by about 29 as the state median age increases.

· decreases by about 29 as the state median age increases.

  (b-2) The 2005 state-by-state crime rate per 100,000   multiple choice 2

· increases by about 20 for every 1,000 new bankruptcies filed.

· decreases by about 20 for every 1,000 new bankruptcies filed.

  (b-3) The 2005 state-by-state crime rate per 100,000   multiple choice 3

· decreases by 0.0322 for each dollar increase in federal funding per person.

· increases by 0.0322 for each dollar increase in federal funding per person.

  (b-4) The 2005 state-by-state crime rate per 100,000   multiple choice 4

· increases by about 30 for each 1% increase in high school graduations.

· decreases by about 30 for each 1% increase in high school graduations.

  (c) Would the intercept seem to have meaning in this regression?   multiple choice 5

· No

· Yes

  (d) Make a prediction for Burglary when X1 = 34 years, X2 = 6.1 bankruptcies per 1,000, X3 = $6,950, and X4 = 64 percent. (Round your answers to 4 decimal places.)   Burglary Rate           $ 

5.  Click here for the Excel Data File

  Choose the dependent variable (the response variable to be "explained") and the independent variable (the predictor or explanatory variable).   (a-1) Dependent Variable    multiple choice 1

· ELOS

· ALOS

  (a-2) Independent Variable    multiple choice 2

· ALOS

· ELOS

  (b) Obtain the regression equation. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)    Y =  X +    (c) Calculate R2. (Round your answer to 4 decimal places.)    R2               (d-1) Zero is contained in the 95% confidence interval.    multiple choice 3

· Yes

· No

  (d-2) The slope is different from zero.    multiple choice 4

· No

· Yes

  (e) Calculate the degrees of freedom and t-critical for a two-tailed t test for zero slope at α = .05. (Round your answers to 2 decimal places.)   

  (f-1) Small p-values tell us the null hypothesis is false.    multiple choice 5

· No

· Yes

  (f-2) The sample provides significant evidence that the slope is positive.    multiple choice 6

· Yes

· No

6. A ski resort asked a random sample of guests to rate their satisfaction on various attributes of their visit on a scale of 1–5 with 1 = very unsatisfied and 5 = very satisfied. The estimated regression model was Y = overall satisfaction score, X1 = lift line wait, X2 = amount of ski trail grooming, X3 = safety patrol visibility, and X4 = friendliness of guest services.  

   (a) Write the fitted regression equation. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign.)   yˆy^ =  +  * LiftWait +  * AmountGroomed +  * SkiPatrolVisibility +  * FriendlinessHosts   (b) Interpret each coefficient.   Overall satisfaction            with an increase in satisfaction for each individual predictor except for friendliness of hosts. (c) Would the intercept seem to have meaning in this regression?   multiple choice 2

· Yes

· No

(d) Make a prediction for Overall Satisfaction when a guest’s satisfaction in all four areas is rated a 4. (Round your answer to 4 decimal places.)   Overall satisfaction score            

7. Use the standard error to construct an approximate prediction interval for Y using an alpha of 5%. (Round your answer to 3 decimal places.)  

Prediction interval for Y: yˆiy^i  ±               Based on the width of this prediction interval, would you say the predictions are good enough to have practical value?    multiple choice