QUESTION 1 [10 marks] Given the following table, use the matrix method to derive the constant and slope parameters of the sample regression function: Productivity index = f(Daily sleep hours). X and Y stand for the daily sleep hours and productivity index respectively. X (Daily sleep hours) Y (Productivity index) 30 4 35 40 6. 65 8 80
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- 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…How do you interpret the R-squared obtained from running this regression?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
- 1. If in a simple linear regression, SST = 315 and the sample correlation coefficient between your dependent and independent variable is 0.96, then the value of SSE is equal to? a. 24.696 b. 290.304 c. 302.4 d. 12.6 e. 0.9216The 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…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.
- How should I interpret the coefficients on a regression with a naural log of a dependent variable? Ex: Ln(wage)=B1+B2Experience+B3Male...+Ui18 Calculate the least square regression líne equation with the given X and Y values. Consider the values: X Y 60 3.1 61 3.6 62 3.8 63 4 65 4.1 To Find, Least Square Regression Line EquationY = a+ b X1. 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) ¹3
- 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.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…100 80 60 Exam score (points) 40 20 0 2 4 6 8 Study time (hours) 10 QUESTION 1: (i) (ii) (iii) Summarize the data in equation form. Construct a table from the data shown on the graph above. Which is the dependent variable and which is the independent variable