Assume that we have the usual Simple Linear Regression model given by: Yi Bo + Bixi +8 Show that in this case: R² = Txy Where is the correlation coefficient between x and y.
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- A 1 Demand 2 WN 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 7.38 8.51 9.52 7.50 9.33 8.28 8.75 7.87 7.10 8.00 7.89 8.15 9.10 8.86 8.90 8.87 9.26 9.00 8.75 7.95 7.65 7.27 8.00 8.50 8.75 9.21 8.27 7.67 7.93 9.26 B PriceDif -0.05 0.25 0.60 0.00 0.25 0.20 0.15 0.05 -0.15 0.15 0.20 0.10 0.40 0.45 0.35 0.30 0.50 0.50 0.40 -0.05 -0.05 -0.10 0.20 0.10 0.50 0.60 -0.05 0.00 0.05 0.55 CTom has been gathering data concerning the cost of a spa treatment, y', during the before Valentine's Day. The only independent variable that he has considered is the number of minutes, "x," in the treatment. Suppose Tom collects data on the relationship between the number of minutes in a treatment and the resulting cost of we the treatment. Tom finds that the correlation between cost and number of minutes is strong and positive. Therefore, he has performed a linear regression analysis on his data. His results are that the constant "a" is 35, and the coefficient "b1" for the independent variable is 1.3. Which of the following is the correct linear regression equation that would allow Tom to predict the cost of a spa treatment given the number of minutes? Oy = 78x + 35 Oy' = 1.3x + 35 %3D Oy = 78x - 1.3 %3D OY = -1.3x - 35***PLEASE INCLUDE EXCEL OUTPUT WITH YOUR RESPONSE
- Select the appropriate interpretation for the slope of the linear regression equation below. Y (Dependent Variable) = Grade Point Average X (Independent Variable) = Average number of hours spent using electronic devices for entertainment purposes yhat = 4 - 0.125*X A. For every 1 hour more spent using electronic devices for entertainment per week then a person's GPA will increase on average by 0.125 points B. For every 1 GPA gained obtained by a student then on average that person will have watched 0.125 hours fewer of entertainment on electronic devices per week C. For every 1 GPA point lost by a student then on average that person will have watched 0.125 hours more of entertainment on electronic devices per week D. For every 1 hour more spent using electronic devices for entertainment per week then a person's GPA will decrease on average by 0.125 pointsAn oil exploration company wants to develop a statistical model to predict the cost of drilling a new well. One of the many variables thought to be an important predictor of the cost is the number of feet in depth that the must be drilled to create the well. Consequently, the company decided to fit the simple linear regression model, where y = cost of drilling the new well (in $thousands) and x = number of feet drilled to create the well. Using data collected for a sample of n=83 wells, the following results were obtained: = 10.5 + 16.20x Give a practical interpretation of the estimate of the slope of the least squares line. An oil exploration company wants to develop a statistical model to predict the cost of drilling a new well. One of the many variables thought to be an important predictor of the cost is the number of feet in depth that the must be drilled to create the well. Consequently, the company decided to fit the simple linear regression model, where y =…It has been hypothesized that overall academic success for first-year college students as measured by grade point average (GPA) is a function of IQ scores = X1, and hours spent studying each week = X2. Suppose the regression equation is: Y = -5.7 + 0.02X1 +0.5X2 1) What is the predicted GPA for a student with an IQ of 100 and 40 hours spent studying per week? 2)Will the independent variables be endogenous? State what it means by endogenous, and explain why that will be the case. 3) If you have a choice to change the variables or add/drop variables, what would be your set of independent variables, and explain why you chose those variables.
- In a study, the simple linear regression equation was found as y = - 2.65 + 3.23 * x. Accordingly, if the value of x is 1.55, what will be the value of "y"? Biraraştımada basit doğrusal regresyon denklemi y-265+3,23xolarak bulunmuştur. Buna yöre xin değeri 1,55 olursa y'nin değeri ne olur?- 25 - O A) -2,36 O B) 2,36 O C) 6,32 O D) -7,66 O E) 7,66A local University conducted a survey of over 2,000 MBA alumni to explore the issue of work-life balance. Each participant received a score ranging from 0 to 100, with lower scores indicating a higher imbalance between work and life. A sample of the data is available below. Let x = average number of hours worked per week and y=work-life balance scale score for each MBA alumnus. Investigate the link between these two variables by conducting a complete simple linear regression analysis of the data. Summarize your findings. E Click the icon to view the data. The least squares regression equation is y =+ (Ox. (Round to two decimal places as needed.) Revenue and Message Rate for Recent Movies Check the usefulness of the hypothesized model. What are the hypotheses to test? O A. H Bo =0 against H: Bo #0 Hours WLB Score 50 75.22 B. H: B, #0 against H: B, =0 45 78.45 OC. H B, = 0 against H B, 0 50 49.68 55 40.11 OD. H Bo#0 against H: Bo =0 50 70.41 60 55.91 Determine the estimate of the…A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using two independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. With this regression model, the predicted price of a 10-year old home with 2,500 square feet of living area is __________. $205.00 $200,000.00 $205,000.00 $255,000.00
- Can a causal relationship be established between a variable y and a variable x by running the following regressions: i) y = f(x) and ii) x = f(y). Explain in less than 75 words.A study tests the effect of earning a Master's degree on the salaries of professionals. Suppose that the salaries of the professionals (S,) are not dependent on any other variables. Let D, be a variable which takes the value 0 if an individual has not earned a Master's degree, and a value 1 if they have earned a Master's degree. What would be the regression model that the researcher wants to test? A. S,= Po + B,D,+u, i=1, .. , n. O B. S,= Po + B, + u, i= 1, .. , n. OC. 1=6o +B1,S, + u, i= 1, .. , n. O D. 0=Bo +B, S, + u,, i= 1, .. , n. Suppose that a random sample of 160 individuals suggests that professionals without a Master's degree earn an average salary of $59,000 per annum, while those with a Master's degree earn an average salary of $80,000 per annum. The OLS estimate of the coefficient B, will be $ and that of B, will be $ Click to select your answer(s). DELLA particular article used a multiple regression model to relate y = yield of hops to x₁ = mean temperature (°C) between date of coming into hop and date of picking and x₂ = mean percentage of sunshine during the same period. The model equation proposed is the following. y = 415.116.6x₁4.50x2+e (a) Suppose that this equation does indeed describe the true relationship. What mean yield corresponds to a temperature of 20 and a sunshine percentage of 39? (b) What is the mean yield when the mean temperature and percentage of sunshine are 19.1 and 42, respectively? You may need to use the appropriate table in Appendix A to answer this question.
