Simple Regression Sales Revenue Year Product Price (P) (millions of pesos) 1 1.20 0.95 1.50 0.93 3 2.00 0.92 4 3.50 0.90 4.10 0.87 6 5.60 0.85 Let Sales Revenue be (v) and Product Price be (x) If the Company intends plans to decrease the product price to PO.82 next year, use simple linear regression to forecast next year's sales revenue. O P43.2112 O P6.6944 O P5.4200 O P44.5327 2.
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Topic: Simple Regression
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- You estimated a regression with the following output. Source | SS df MS Number of obs = 289 -------------+---------------------------------- F(1, 287) = 41986.64 Model | 664544048 1 664544048 Prob > F = 0.0000 Residual | 4542496.25 287 15827.5131 R-squared = 0.9932 -------------+---------------------------------- Adj R-squared = 0.9932 Total | 669086544 288 2323217.17 Root MSE = 125.81 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 43.81013 .2138056 204.91 0.000 43.38931 44.23096 _cons | 49.31707 16.96222 2.91 0.004 15.93094 82.70319…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?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.
- Consider the following OLS regression results, In(inc)=1.970+.083educ, R2=.186, where inc represents annual income (in $1000s) and educ represents years of education. The R² can be interpreted as .186% of the variation in annual income is explained by years of education. .186% of the variation in log annual income is explained by years of education. O 18.6% of the variation in annual income is explained by years of education. O 18.6% of the variation in log annual income is explained by years of education.Sales in a company are $188 million in 2009 and increase $208 million in 2010. Compute the percentage increase in sales using the usual formula Compare this value to the approximation The approximation performs (1) percentage change increases. 100 x (1) O better (2) O deteriorates O worst O improves 100 x 100 x (Sales 2010 - Sales 2009) Sales 2009 100 x [In (Sales2010) -In (Sales2009)] (Sales 2010 - Sales2009) Sales 2009 100 x [In (Sales 2010) -In (Sales2009)] = [ (Express your response as a percentage and round to three places) Now, assume that sales in a company are $188 million in 2009 and increase $264 million in 2010. = (Sales2010 - Sales 2009) Sales 2009 % % % 100 x [In (Sales 2010) -In (Sales 2009)] = [ (Express your response as a percentage and round to three places) % when the change is small. The quality of the approximation (2). as theThe 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
- You estimated the following regression. What value would you predict for Y, if X = 81? (Round your final answer to zero decimal places.) Source | SS df MS Number of obs = 204 -------------+---------------------------------- F(1, 202) = 406.05 Model | 6131684 1 6131684 Prob > F = 0.0000 Residual | 3050340.21 202 15100.6941 R-squared = 0.6678 -------------+---------------------------------- Adj R-squared = 0.6661 Total | 9182024.21 203 45231.6463 Root MSE = 122.88 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 40.27997 1.998931 20.15 0.000 36.33853 44.22142 _cons | 192.9333 120.837 1.60 0.112…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…Setting: U.S. Auto manufacturers are trying to develop a multivariate function with which to estimate the demand for their gas-electric hybrid compact cars. Here is one that Motors General developed for its Jolt: Qj = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A Where Qj = the number of Jolts demanded per week. Pj = the price of each new Jolt (in $). Pf = the price of each new Ford gas-electric hybrid (in $). Pt = the price of each new Toyota gas-electric hybrid (in $). Pb = the price of replacement batteries for the Jolt (in $). Tc = the amount of tax credit incentive offered with the purchase of a new hybrid (in $). Y = average weekly disposable income of a typical Jolt purchaser (in $). Mg = the miles per gallon of gas rating of the Jolt (in miles per gallon). A = average weekly Jolt advertising expenditure (in $). 6 If all variables remain unchanged except that the price of the Toyota hybrid (Pt) decreases by $500, then the demand for Jolts will: 7…
- 2. Consider the following estimated regression equation (standard errors in parentheses): Yi-120+ 0.10Ft + 5.33Rt (0.05) (1.00) R² = 0.5 i. ii. iii. where A Yi = the corn yield (bushels/ha) in year t Ft = fertilizer intensity (pounds/ha) in year t Rt = rainfall (inches) in year t Interpret the meaning of the intercept. Suppose you are told that the true value of BF (coefficient on fertilizer intensity) is known to be 0.20. Does this show that the estimate is biased? Why or why not? Suppose you were told that the equation does not meet all the classical assumptions and, therefore, the OLS estimator used is not BLUE. Does this mean that the true BR (coefficient on rainfall) is definitely not equal to 5.33? Why or why not?All questions utilize the multivariate demand function for Smooth Sailing sailboats in C6 on text page 83. Compute to three decimal places. Initial values are: PX = $9500 PY = $10000 I = $15000 A = $170000 W = 160 This function is: Qs = 89830 -40PS +20PX +15PY +2I +.001A +10W 1.(a). Use the above to calculate the arc price elasticity of demand between PS = $9000 decreasing to PS = $8000. The arc elasticity formula is: 1.(b). Judging from the computation in (a), do you expect the revenue resulting from the decrease in Ps to $8000 to increase, remain the same, or decrease relative to the revenue at Ps = $9000. (Hint: see the table on page 65 of Truett). Explain your choice. 1.(c). Calculate the point elasticity of demand for Smooth Sailing sailboats at PS = $9000 (which should make Qs = 101600). The formula is: 1.(d). Does this elasticity value indicate that Smooth Sailing demand is relatively responsive to changes in the price of these sailboats? Explain…D. MoviefliX, an online movie streaming service that offers a wide variety of award-winning TV shows, movies, animes, and documentaries would like to determine the mathematical trend of memberships in order to project future needs. Year 2013 2014 2015 2016 2017 2018 2019 2020 2021 Membership 17 16 16 21 20 20 23 25 24 (000s) (i) Use the following time series data, to develop a regression equation relating memberships to time. (ii) Forecast 2023 membership.