From 10 observations of price (m) and supply (n) of a commodity, the fóllowing summary figures were obtained (in appropriate units) : Σm= 130 ; Σn= 220 ; Σ mr=2288 ; Σην= 5506 and Σ mn= 3467 Compute a line of regression of n on m and estimate the supply when the price is 16.
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- In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 18.6 + 3.7x, - 2.2x2 + 7.9x3 + 2.6x4 (a) Interpret b, in this estimated regression equation. = 3.7 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x, are held constant. = -2.2 is an estimate of the change in y corresponding to a 1 unit change in x, when x2, x3, and x are held constant. O b1 = 7.9 is an estimate of the change in y corresponding to a1 unit change in x, when x,, x2, and x, are held constant. O b, O b, = 3.7 is an estimate of the change in y corresponding to a 1 unit change in x, = 2.6 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x3 are held constant. when and x4 are held constant. Interpret b, in this estimated regression equation. O b2 = 2.6 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x, are held constant. = 7.9 is an estimate…Murray's Petroleum Company is trying to formulate a cost function for operating expenses in orde to predict the future costs. The following information was ascertained from past operations: ΣΧ 40 ΣΧΥ EX² ΣΎ2 1434 n 10 From the following information, calculate the following using regression analysis (show all working A. variable cost per unit B. fixed cost C. cost function D. total cost if 2000 litres are produced ΣΥ 120 466 234To assess the relationship between monthly sales of a product and monthly advertising expenditure(both in thousands of dollars); a linear regression model was fitted using data for 20 months and results were as follows: s.e(8) Variable B Intercept 6.3812 advert 1.1762 0.0786 (a) From the results, we can say that an increase of 1000 dollars in monthly expenditure is associated with an increase of 1.1762 dollars in average sales. an increase of 1.1762 dollars in monthly expenditure is associated with an increase of one dollar in average selling price. an increase of 1000 dollars in monthly expenditure is associated with an increase of 1176.2 dollars in average sales. an increase of one dollar in monthly expenditure is associated with an increase of 1.1762 dollars in average sales. <
- Given the following values: X = 20; xy = 400; y2 = 600; y = 15; obtain the regression equation of x on y? O a. x= 0.66y - 29.9 O b. x= 0.66y + 10.1 Осх- 0.66у - 10.1 O d. x= 0.66y + 29.9A researcher is interested in finding out the factors which determined the yearly spending on family outings last year (Y, measured in dollars). She compiles data on the number of members in a family (X1), the annual income of the family (X2), and the number of times the family went out on an outing in the last year (X3). She collects data from 196 families and estimates the following regression: Y=120.45+1.54X1+2.12X2+2.12X3. Suppose β1, β2, β3, denote the population slope coefficients of X1, X2, and X3, respectively. The researcher wants to check if neither X1 nor X2 have a significant effect on Y or at least one of them has a significant effect, keeping X3 constant. She calculates the value of the F-statistic for the test with the two restrictions (H0: β1=0, β2=0 vs. H1: β1≠0 and/or β2≠0) to be 3.00. The p-value for the test will be enter your response here?Q.4. Obtain the equation of the line of regression of y on x from the following data and estimate the blood pressure when the age is 50 years. Age in years x Blood pressure y 50 142 40 120 71 162 35 110 60 140 45 125 52 155 47 140 36 111 40 135 65 150 59 153
- The following data on x maternal age in years of the young birth mothers and y = weight of baby born in grams summarizes the result of a study. Assume that a simple linear regression model y = Bo + B1x + e is an appropriate model for the study. x-bar = 17 (avg of x's) y-bar = 3004.1 (avg of y's) SSx = 20 SSxy %3D 4903 SSw 1539182.9 n 10 Calculate the value of s-(standard error of regression) and enter the answer to the nearest tenth (1 decimal place).When using population size as the explanatory variable, x, and broadband subscribers as the response variable, y, for data on the number of individuals in a country with broadband access and the population size for 36 nations, the regression equation is y = 4,975,098 +0.0342x. a. Interpret the slope of the regression equation. Is the association positive or negative? Explain what this means. b. Predict broadband subscribers at the (i) population size 7,014,655, (ii) population size 1,155,173,053. c. For one nation, y = 71,110,000, and x = 322,413,902. Find the predicted broadband use and the residual for this nation. Interpret the value of this residual. a. Since the association is positive, the slope means that as the (Type an integer or a decimal.) b. (i) The predicted broadband subscribers for population size 7,014,655 is (Round to the nearest whole number as needed.) population size increases by 1 unit, the number of broadband subscribers tends to increase by 0.0342.The table lists the average monthly cost to workers for family health insurance for various years. Year, x Average Monthly Cost to Workers for Family Health Insurance $298 a) Use a graphing calculator to fit a regression line to the data. b) Predict the average monthly cost to workers for family health insurance in 2020, and compare the value with $493.3, which is obtained using the points (1,340) and (4,386). c) Find the correlation coefficient for the regression line, and determine whether the line fits the data closely. 2009, 0 2010, 1 2011, 2 340 348 2012, 3 367 2013, 4 2014, 5 386 406 a) The linear equation of the regression line that best models the data is y =x+. (Round to the nearest hundredth as needed.) b) The average monthly cost to workers for family health insurance in 2020 is predicted to be $ (Round to the nearest cent as needed.) Compare the above obtained value with $493.3 This value is $ $493.3 c) The correlation coefficient is (Round to the nearest thousandth as…
- The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x₁) and newspaper advertising (x₂). The estimated regression equation was ŷ = 83.5+ 2.21x₁ + 1.80x₂. The computer solution, based on a sample of eight weeks, provided SST = 25.4 and SSR = 23.495. (a) Compute and interpret R² and R2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R² = 0.653 and R2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis ---Select--- preferred since both R² and R2 show ---Select--- ✓percentage of the variability of y explained when both independent variables are used. . Adjusting for the number of…Consider the following regression equation representing the linear relationship between the Canada Child Benefit provided for a married couple with 3 children under the age of 6, based on their annual family net income: ŷ =121.09−0.57246xR2=0.894 where y = annual Canada Child Benefit paid (in $100s) x = net annual family income (in $1000s) Source: Canada Revenue Agency a. As the net annual family income increases, does the Canada Child Benefit paid increase or decrease? Based on this, is the correlation between the two variables positive or negative?The Canada Child Benefit paid .The correlation between the two variables is .b. Calculate the correlation coefficient and determine if the relationship between the two variables is strong, moderate or weak.r= , the relationship is . Round to 3 decimal places c. Interpret the value of the slope as it relates to this relationship. For every $1 increase in annual family net income, there is a $0.57246 decrease in…Assume there is a positive linear correlation between the variable R (Return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R= 2.3t + 4.8 A. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? B. If the investment continues to grow at a constant rate, what is the expeted return rate when the investment is 7 years old? C. If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?