Perform a linear regression that relates bar sales to guests (not to time). b) If the forecast is for 20 guests next week, what are the sales expected to be?
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The following data relate the sales figures of restaurant, to the number of customers registered that week:
|
Week |
Customers |
Sales (SR) |
|
First |
16 |
330 |
|
Second |
12 |
270 |
|
Third |
18 |
380 |
|
Fourth |
14 |
300 |
- a) Perform a linear regression that relates bar sales to guests (not to time).
- b) If the
forecast is for 20 guests next week, what are the sales expected to be?
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- You estimated a regression with the following output. Source | SS df MS Number of obs = 223 -------------+---------------------------------- F(1, 221) = 17592.99 Model | 182392130 1 182392130 Prob > F = 0.0000 Residual | 2291176.96 221 10367.3166 R-squared = 0.9876 -------------+---------------------------------- Adj R-squared = 0.9875 Total | 184683307 222 831906.786 Root MSE = 101.82 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 11.97037 .0902481 132.64 0.000 11.79252 12.14823 _cons | 74.40159 10.96696 6.78 0.000 52.78839 96.01479…Given the regression equationY = 43 + 10Xa. What is the change in Y when X changes by +8?b. What is the change in Y when X changes by -6?c. What is the predicted value of Y when X = 11? d. What is the predicted value of Y when X = 29? e. Does this equation prove that a change in X causes a change in Y?Given the regression equationY = -50 + 12Xa. What is the change in Y when X changes by +3?b. What is the change in Y when X changes by -4?c. What is the predicted value of Y when X = 12?d. What is the predicted value of Y when X = 23?e. Does this equation prove that a change in X causes a change in Y?
- Past class data has shown that the regression line relating the final exam score and the midterm exam score for students who take statistics from the College of Information Technology and Engineering from Dr. Kalaw is: final exam = 50 + 0.5 × midterm One interpretation of the slope is a. students only receive half as much credit (.5) for a correct answer on the final exam compared to a correct answer on the midterm exam. b. a student who scored 0 on the midterm would be predicted to score 50 on the final exam. c. a student who scored 10 points higher than another student on the midterm would be predicted to score 5 points higher than the other student on the final exam. d. a student who scored 0 on the final exam would be predicted to score 50 on the midterm exam.Test Design: Suppose I want to test the impact of soccer coaches on soccer teams. How would you test this? Include a few (3 or 4) independent variables to explain the dependent variable. Describe the data and write the regression equation.In exercise 1, the following estimated regression equation based on 10 observations was presented. y^=29.1270+.5906x1+.4980x2Here SST=6724.125, SSR=6216.375, sb1=.0813, and sb2=.0567. a) Compute MSR and MSE. b) Compute F and perform the appropriate F test. Use α=.05. c) Perform a t test for the significance of β1. Use α=.05. d) Perform a t test for the significance of β2. Use α=.05.
- Econometrics: Given the following regressions: yt = 1.2yt-1 + Et and xt = 1.3xt-1 - 0.4xt-2 + Ct 1) Find he homogeneous equation and assess the implications of the roots.You estimated the following regression. What value would you predict for Y, if X = 42? (Round your final answer to zero decimal places.) Source | SS df MS Number of obs = 303 -------------+---------------------------------- F(1, 301) = 52790.25 Model | 510753802 1 510753802 Prob > F = 0.0000 Residual | 2912221.36 301 9675.15401 R-squared = 0.9943 -------------+---------------------------------- Adj R-squared = 0.9943 Total | 513666023 302 1700880.87 Root MSE = 98.362 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 17.14603 .0746254 229.76 0.000 16.99918 17.29289 _cons | 56.37208 8.600915 6.55 0.000…Numerical Answer Only Type Question Enter the numerical value only for the correct answer in the blank box. If a decimal point appears, round it to two decimal places. Assume that the number of visits by a particular customer to a mall located in downtown Toronto is related to the distance from the customer's home. The following regression analysis shows the relationship between the number of times a customer visits(Y)per month and the distance(X, measured in km) from the customer's home to the mall. \[ Y=15-0.5 X \] A customer who lives30 kmaway from the mall will visi______ who lives10 km away. less times than a customer
- The following gives the number of accidents that occurred on Florida State Highway 101 during the last 4 months: Jan Feb Mar AprMonth 1 2 3 4Number of Accidents 30 40 70 105 Using the least-squares regression method, the trend equation for forecasting is (round your responses to two decimal places): y = ? + ?x(10+05)The following data were collected on the height (inches) and weight (pounds) of women swimmers.Height6870646566 Weight132110106115128 a. Develop the estimated regression equation by computing the values of b0 and b1.DEPENDENT VARIABLE Qc R- SQUARE P- VALUE ON F 64 0.8093 0.0001 INDEPENDENTVARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 8.20 4.01 2.04 0.0461 PC -3.54 1.64 -2.16 0.0357 M 0.64287 0.19 3.38 0.0014 PA 0.7854 0.38 2.07 0.0439 10. Write the resulting regression equation. Q = f( P, M, PR) where Qc = demand for cement/month (in yards) Pc = the price of cement per yard, M = country’s tax revenues per capita, and PR = the price of asphalt per yard.