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.
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- Consider the following data regarding students' college GPAs and high school GPAs. The estimated regression equation is Estimated College GPA=1.85+0.4743(High School GPA).Estimated College GPA=1.85+0.4743(High School GPA). GPAs College GPA High School GPA 3.843.84 2.562.56 3.573.57 3.903.90 2.072.07 3.143.14 4.004.00 3.223.22 3.873.87 2.882.88 2.212.21 2.082.08 Copy Data Step 1 of 3 : Compute the sum of squared errors (SSE) for the model. Round your answer to four decimal places.Consider the simple regression model: y=0.56+1.56x+u Using this and assuming the estimated Var(y)=0.64 and the estimated Var(x)=3.07, what is the estimated Var(x+y)?True or False For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable.
- Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary=11,722.40+3182.56(Education)+1202.44(Experience)Estimated Salary=11,722.40+3182.56(Education)+1202.44(Experience) Suppose an employee with 66 years of education has been with the company for 33 years (note that education years are the number of years after 8th8th grade). According to this model, what is his estimated annual salary?Suppose you run the following regression: outcome=alpha0 + alpha1*female + alpha2*married + epsilon. You know that female equals 1 for females and 0 otherwise. You know that married equals 1 if the person is married and 0 otherwise. What is the estimated outcome for married females?The table below shows the number, in thousands, of vehicles parked in the central business district of a certain city on a typical Friday as a function of the hour of the day. Hour of the day Vehicles parked(thousands) 9 A.M. 6.2 11 A.M. 7.4 1 P.M. 7.5 3 P.M. 6.6 5 P.M. 3.9 (a) Use regression to find a quadratic model for the data. (Let V be the number of vehicles and t be the time in hours since midnight. Round the regression parameters to three decimal places.) V = (b) Express using functional notation the number of vehicles parked on a typical Friday at 4 P.M., and then estimate that value. (Round your answer to two decimal places.) V = = thousand
- The following data relate the sales figures of the bar in Mark Kaltenbach's small bed-and-breakfast inn in portland, to the number of guest registered that week: week guests bar sales 1 16 $330 2 12 $270 3 18 $380 4 14 $315 a) The simple linear regression equation that relates bar sales to number of guests(not to time) is (round your responses to one decimal place): Bar sales = [___]+[___]X guestsA manufacturer is developing a facility plan to provide production capacity for its factory. The amount of capacity required in the future depends on the number of products demanded by its customers. The data below reflect past sales of its products: Year Annual Sales (number of products) Year Annual Sales (number of products) 1 490 5 461 2 487 6 475 3 492 7 472 4 478 8 458 Use simple linear regression to forecast annual demand for the products for each of the next three (3) years, by using the tabular method to: derive the values for the intercept and slope derive the linear equation plot the linear regression line develop a forecast for the firm’s annual sales for each of the next three yearsIn a regression problem with one output variable and one input variable, we set up two cutpoints z1 and z2 for the input variable and we fit a step function regression model based on these two cutpoints of the input variable. If you write the regression problem in matrix form y = X%*%β + ε, how many rows would the vector β have?
- Suppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+εY=α+βaA+βpP+ε Now suppose that the estimate of the model produces following results: α=344.585α=344.585, ba=0.102ba=0.102, bp=−11.192bp=−11.192, sba=0.173sba=0.173, sbp=4.487sbp=4.487, R2=0.813R2=0.813, and F-statistic=11.361F-statistic=11.361. Note that the sample consists of 10 observations. 1.) According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures decrease or increase sales by approximately 102,813 or 11,192 gallons. Similarly, a $1 increase in the selling price decrease or increase sales by approximately 813,11,192 or 102 gallons. 2.)Which of the independent variables (if any) appears to be statistically significant (at the 0.05…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.Using the data below, what is the slope coefficient from a regression of Quantity on Price? It is probably easiest to use either Gretl or Jamovi as in the powerpoint example. (round your answer to the nearest 0.1, and it can be either positive or negative.) Quantity 17 24 23 39 55 54 60 76 71 80 Price 93 77 62 64 47 35 38 12 29 2