3. To explain what determine the price of air conditioners, B.T. Ratchford, obtained the following regression results based on a sample of 19 air conditioners: R²=0.84 y=-68.236 +0.023x, +19.729x3, +7.653x (0.005) (8.992) (3.082) se= Where y the price, in dollars x2= the BTU rating of air conditioner x3 the energy efficiency ratio x, the number of settings se standard errors a) Interpret the regression results. b) Do the results make economic sense? c) At 5% significance level, test the hypothesis that the BTU rating has no effect on the price of an air conditioner vs. that it has a positive effect. d) Would you accept the null hypothesis that the three explanatory variables explain a substantial variation in the prices of air conditioners? Show clearly all your calculations.
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- QUESTION 1 Suppose a researcher collects data on houses that have been sold in a particular neighbourhood over the past year, and obtains the regressions results in the table shown below. This table is used for Questions 1-6. Dependent variable: In(Price) Regressor (1) (2) (3) (4) (5) 0.00042 (0.000038) Size In(Size) 0.57 (2.03) 0.69 0.68 0.69 (0.055) (0.054) (0.087) In(Size)² 0.0078 (0.14) Bedrooms 0.0036 (0.037) Рol 0.082 0.071 0.071 0.071 0.071 (0.032) (0.034) (0.034) (0.036) (0.035) 0.037 0.027 0.026 0.027 0.027 (0.030) View (0.029) (0.028) (0.026) (0.029) Pool x View 0.0022 (0.10) 0.12 (0.035) Condition 0.13 0.12 0.12 (0.035) 0.12 (0.045) (0.035) (0.036) 6.63 (0.53) Intercept 10.97 6.60 7.02 6.60 (0.069) (0.39) (7.50) (0.40) Summary Statistics SER 0.102 0.098 0.099 0.099 0.099 R? 0.72 0.74 0.73 0.73 0.73 Variable definitions: Price = sale price ($); Size = house size (in square feet); Bedrooms = number of bedrooms; Pool = binary variable (1 if house has a swimming pool, 0…As an auto insurance risk analyst, it is your job to research risk profiles for various types of drivers. One common area of concern for auto insurance companies is the risk involved when offering policies to younger, less experienced drivers. The U.S. Department of Transportation recently conducted a study in which it analyzed the relationship between 1) the number of fatal accidents per 1000 licenses, and 2) the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Your first step in the analysis is to construct a scatterplot of the data. FIGURE. SCATTERPLOT FOR U.S. DEPARTMENT OF TRANSPORATION PROBLEM U.S. Department of Transportation The Relationship Between Fatal Accident Frequency and Driver Age 4.5 3.5 3 2.5 1.5 1 0.5 6. 10 12 14 16 18 Percentage of drivers under age 21 Upon visual inspection, you determine that the variables do have a linear relationship. After a linear pattern has been established visually, you now proceed with performing linear…As the selling price of a product increases, demand decreases. Fewer people will buy a product if it is more expensive. This is a very important concept. The demand equation for new iSmarts is given by 0.025x , where p is the unit p = 100 price (in dollars) of the iSmart and x is the number of units produced. We can determine the total revenue (money earned for selling x iSmarts) by multiplying the number of items we sell, x and the price p. The total revenue obtained by producing and selling x iSmarts is given by = xp 100x – 0.025x². It makes sense that this function is quadratic. The company can price the iSmarts so high that no one will buy them and the revenue will be zero. The can also set the price to $0, but the revenue will still be $0, no matter how many iSmarts they "sell". In between, the graph is a parabola opening downward. Determine prices p that would keep revenue above 6530 dollars. Give your answers to 2 decimal places. The revenue will be above 6530 if price is…
- Water is being poured into a large, cone-shaped cistern. The volume of water, measured in cm³, is reported at different time intervals, measured in seconds. A regression analysis was completed and is displayed in the computer output. Regression Analysis: cuberoot (Volume) versus Time Predictor Coef SE Coef Constant -0.006 0.00017 -35.294 0.000 Time 0.640 0.000018 35512.6 0.000 s=0.030 R-Sq=1.000 R-sq (adj)=1.000 What is the equation of the least-squares regression line? Volume = 0.640 - 0.006(Time) Volume = 0.640 - 0.006(Time) Volume = -0.006 + 0.640(Time) Volume = - 0.006 + 0.640(Time?)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 customerConsider the output here from a regression in R. What is 3₂? Coefficients: Estimate (Intercept) 1.708 5.404 -1.478 9.531 X1 X2 X3 Std. Error 0.555 2.792 0.6 2.758
- 1. Consider a linear regression model y = XB + € with E(e) = 0. The bias of the ridge estimator of 3 obtained by minimizing Q(B) = (y — Xß)¹ (y — Xß) + r(BTB), for some r > 0, is ——(X²X + r1)-¹8 1 (X¹X +rI)-¹3 r -r(XTX+rI) ¹8 r(X¹X+r1) ¹3The 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?Q4. The Omantel firm has estimate the Sales of fibre internet connections in Oman with the related to advertising expenditure made by the company over the past 26 months. Following is the firm estimated results of the regression equation. DEPENDENT VARIABLE: Y R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 26 0.85121212 8.747 0.0187 PARAMETER STANDARD VARIABLE ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 7.6 6.33232 1.200 0.2643969 3.53 0.52228 ? 0.0001428 a. What is the dependent and independent variables in the above regression equation of Omantel firm? b. Calculate the estimated t-ratio. Test the slope estimates for statistical significance at the 10 percent significance level. d. Interpret the coefficient of determination.
- The table to the right contains price-demand and total cost data for the production of projectors, where p is the wholesale price (in dollars) of a projector for an annual demand of x projectors and C is the total cost (in dollars) of producing x projectors. Answer the following questions (A) - (D). (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. X 270 360 520 780 The fixed costs are $. (Round to the nearest dollar as needed.) ITTI y = (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.) Use the linear regression equation found in the previous step to estimate the fixed costs and variable costs per projector. The variable costs are $ per projector. (Round to the nearest dollar as needed.) (C) Find the break even points. The break even points are (Type ordered pairs. Use a comma to separate answers as needed. Round to the nearest integer as…You estimated a regression with the following output. Source | SS df MS Number of obs = 335 -------------+---------------------------------- F(1, 333) = 69555.83 Model | 211169628 1 211169628 Prob > F = 0.0000 Residual | 1010979.01 333 3035.97301 R-squared = 0.9952 -------------+---------------------------------- Adj R-squared = 0.9952 Total | 212180607 334 635271.28 Root MSE = 55.1 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 44.15183 .1674102 263.73 0.000 43.82251 44.48114 _cons | 31.63715 16.49849 1.92 0.056 -.8172452 64.09155…Consider the following data regarding students' college GPAs and high school GPAs. The estimated regression equation is GPA). Estimated College GPA = 2.56 + 0.1582 High School GPA GPAs College GPA High School GPA 3.96 4.42 2.81 3.91 3.53 4.21 3.27 2.76 3.58 4.95 2.07 4.24 Copy Data Step 2 of 3: Compute the mean square error (s2) for the model. Round your answer to four decimal places.