(1) E[ Y] = β + βιX, Var(Y) = ΟΣ-ΣΥ i=1
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Show that the following formula is established in a simple linear regression model.
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- Explain the concept of Linear Regression with Multiple Regressors?Please show work in excel Stars Co. wants to advertise its products in the hope that more advertising will result in more sales. The following data have been collected in the past year showing money spent on advertising in a month and sales on the same month: a) Develop a regression equation to forecast the Sales as a function of the Advertising by drawing a scatter chart in Excel. b) Suppose that the company would like to advertise in the amount of 30 thousands. Estimate the Sales in response to this amount of advertising. Month Sales (Thousands) Advertising (Thousands) Jan 1200 30 Feb 1100 25 March 1220 32 April 990 23 May 1190 31 June 1050 24 July 770 22 Aug 1080 28 Sept 1220 33 Oct 1140 25 Nov 740 19 Dec 790 20A study was conducted to see whether heart rate (y) on swimmers linearly related to their age (x1) and swimming time for 2000 meters (x2). A random sample of ten swimmers was selected and the result is shown in the following Microsoft Excel output. (a)Interpret the value of R2 from the output. (b)Conduct a hypothesis test to test whether the linear regression model is fit or not using a = 0.05. (c)Calculate the 95% confidence interval for the coefficient value for age.
- A 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 $255,000.00A 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). DELL
- A biologist is interested in predicting the percentage increase in lung volume when inhaling (y) for a certain species of bird from the percentage of carbon dioxide in the atmosphere (x). Data collected from a random sample of 20 birds of this species were used to create the least-squares regression equation ŷ = 400-0.08x. Which of the following best describes the meaning of the slope of the least-squares regression line? (A) The percentage increase in lung volume when inhaling increases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (B) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on average, for every 1 percent increase in lung volume when inhaling. (C) The percentage increase in lung volume when inhaling decreases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (D) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on…Consider the simple linear regression model Wage = Bo + B1*Age + U. The error term U can capture the followings, with the exception of O A. possible measurement error in Wage. O B. the temperature in London Ontario tomorrow. O C. possible model misspecification, such as the nonlinear effect of Age on Wage. O D. other variables that affect the dependent variable, such as previous work experience.Show that the following relationship on the simple linear regression class notebook is true: (Refer the image)
- If you know that the equation of the simple linear regression between the final exam result and the mid-year examination result for students in engineering statistics is as follows: Final exam = 50 + 0.5 x midterm according to the above equation, then the regression coefficient is:Linear regression is a highly effective data analysis method that accurately estimates the value of unknown data using related and known data. This is achieved using a linear equation that accurately models the quantitative relationship between the dependent (unknown) and independent (known) variables. In other words, by looking at how one variable affects another, this method can accurately forecast the value of the dependent variable. It involves choosing the variable to forecast and using another variable to make informed predictions about its value. In experiments, the independent variable is the cause, and its value remains constant while other variables have been modified. On the other hand, the dependent variable is the effect, and changes influence its value in the independent variable. As I began my business, I struggled with determining the appropriate pricing for my products. It was important that the prices were reasonable while allowing for a profit. The pricing had to…In Step 2: Construct an estimated simple linear regression model how did you come up with the column X*X ?
