Consider the linear regression of the variable "balance" as output and the variables "student" and "income" as input variables (from the dataset Default in ISLR2). What is the L1-norm of the regression coefficients, which is the sum of the absolute values of the coefficients?
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- What is the functional form of this equation? What are the advantages and limitations of this functional form? Interpret precisely the coefficients of Px and Py in the regression.XYZ company is interested in quantifying the impact of consumer promotions on the sales of its packaged food product. XYZ has historical data on the following variables for 38 weeks: • Sales: Weekly sales volume in thousands of units.• Prom: Weekly spending on consumer promotions in thousands of Dollars" "A regression analysis was applied to XYZ historical dataset. The dependent variable is weekly Sales and the independent variables are weekly Prom and weekly Lagged Prom (i.e., last week Prom). This is a summary of the regression output:Sales = 0.80 + 1.20*Prom - 0.40*Lag(Prom) • R-squared=0.85• F-Statistic=23.83• p-value=0.001 (for the overall regression)•All regression coefficients are statistically significant at the 5% level." A. What will be the predicted sales volume ? B. What is the gross margin of this net volume impact due to $1000 spending per week on consumer promotions, if brand makes $2.20 gross margin per unit . C. What is the ROI of this promotion? D. What is predicted…A simple regression analysis to estimate the demand for Chick-fil-A’s new premium super-sized spicy chicken sandwich is Q= 48-2p. If Chick-fil-A sets the price at $12 and Q=20, calculate the regression’s error term? Also, list five assumptions of the classical linear regression model.
- Questions 1-30 refer to the following scenario: A company reports bi-annual (twice a year) sales data. The sales data for the last three years is shown in below Table. The residual sum of squares of the regression is RSS = a 50 b 70 c 120 d 20 The total sum of squares of the regression is TSS = a 20 b 120 c 70 d 50 The R-squared of the regression is R2= a 0.78 b 0.68 c 0.58 d 0.88 The mean sum of squares of the regression is Mean ESS = a 20 b 50 c 120 d 70 The mean sum of squares of the residuals is Mean RSS = a 12.5 b 15.0 c 7.5 d 10.0 You want to test whether the regression in its entirety explains something which is different from zero. For this purpose you use a a Chi-squared test b T-test c E-test d F-test The value for testing the explanatory significance of the entirety of the regression is a 7.6 b 5.6 c 6.6 d 8.6 The…Question 15 When the R2 of a regression equation is very high, it indicates that all the coefficients are statistically significant. the intercept term has no economic meaning. a high proportion of the variation in the dependent variable can be accounted for by the variation in the independent variables. there is a good chance of serial correlation and so the equation must be discarded.Consider a data set with 15 observations and consider a multiple linear regression model with 7 in-dependent variables. Assume you have estimated the model and you find that SST = 1,325 and SSR = 794.
- The Weibracht Corporation designs and manufactures custom beer steins for some of the numerous brew pubs in western North Carolina. Each stein costs Weibracht $8 to produce. The brew pubs purchase the steins from Weibracht for resale to their customers and require a 51% margin. Weibracht’s marketing director has conducted a regression analysis using historical data, resulting in the following regression line: q = -12 * p + 326, where q = slope * retail price + MWB What is the profit maximizing price that Weibracht should charge the brew pubs for these custom steins?From the following data, determine if the data has a positive or a negative relationship with each other. Showcase the regression line, and determine if the data provided fits the approximate curve.Questions 1-30 refer to the following scenario: A company reports bi-annual (twice a year) sales data. The sales data for the last three years is shown in below Table. The intercept (a) of the regressions line (DV: Sales, IV: Obs) is equal to A 2 B 4 C 3 D 1 The slope (b) of the regressions line (DV: Sales, IV: Obs) is equal to a 4 b 2 c 3 d 1 The standard error of the regression is a 5.34 b 3.54 c 4.35 d 2.51 The standard error of the intercept is a 1.30 b 2.30 c 0.30 d 3.30 You want to test the hypothesis that the intercept is statistically significantly different from zero. To do so, you use the attached t-table. Your alpha (the risk you accept to make a Type I error) is a=0.1. How many degrees of freedom do you have? a n b n-2 c 4 d both b. and c. are correct You want to test the hypothesis that the intercept…
- Suppose that an economist has been able to gather data on the relationship between demand and price for a particular product. After analyzing scatterplots and using economic theory, the economist decides to estimate an equation of the form Q= aPb, where Q is quantity demanded and P is price. An appropriate regression analysis is then performed, and the estimated parameters turn out to be a = 1000 and b = - 1.3. Now consider two scenarios: (1) the price increases from $10 to $12.50; (2) the price increases from $20 to $25. a. Do you predict the percentage decrease in demand to be the same in scenario 1 as in scenario 2? Why or why not? b. What is the predicted percentage decrease in demand in scenario 1? What about scenario 2? Be as exact as possible.Suppose you have run four regression models: A, B, C, and D. You are going to make a decision on which one to use just based on the adjusted r² value. Here are the adjusted r² values for each model: A: 0.71 B: 0.57 C: 0.65 D: 0.76 Which regression model would you choose based on the adjusted r²? OD since it has the highest adjusted r² value B since it has the lowest adjusted r² OC since it has an adjusted r² between the adjusted r² of regressions B and D. Either B or C since they have the lowest adjusted r²The 2008 sales and profits of seven companies were given as follows Firm Sales ($ Billions) Profit ($ Billions) Fiat 5.7 0.27 Honda 6.7 0.12 BP 0.2 0.01 Toyota 0.6 0.04 Apple 3.8 0.05 IBM 12.5 0.46 Phillips 0.5 0.02 The estimated value for the company’s Profit can be estimated using the equation; Y ̂i = α ̂ + β ̂Xi……………………………………………………………………Eqn.1 Where; Y = Companies Profit X = Companies Sales α ̂ and β ̂ are estimated parameters in the model Calculate the sample regression line, where profit is the dependent variable (Y) and sales is the independent variable (X)