3 I. Show complete solutionsSimple Linear Regression and Correlation:a.) Results of a study on the occurence of sodium and chloride in surface streams in acoastal area. The following data are chloride concentration (y) in mg/liter and road-wayarea in the watershed (x) in %.Y0.244.60.36.40.459.80.7510.70.5710.60.7510.90.411.70.812.50.6140.7814.70.8515.10.6818.30.6919.21.423.11.1527.31.0527.71.69321.6238.4

The independent variable is road-way area in the watershed. The dependent variable is chloride…

Answered: 3 I. Show complete solutions Simple…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the following simple linear regression model between the dependent variable, SALES (reflecting monthly sales, in thousands of dollars) and independent variable, ADVERTISING (representing the monthly advertising expenditure, in thousands of dollars): Expected (SALES) = 4.2 - 2.6 ADVERTISING. The value 2.6 in the above regression model represents: A. the value of SALES, on average, when ADVERTISING is zero. B. the change in SALES following a unit decrease in ADVERTISING. C. a ratio of SALES over ADVERTISING as a percentage. D. the proportion of the variation in SALES explained by using ADVERTISING in the regression equation. E. a ratio of ADVERTISING over SALES as a percentage.
To 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. <
A study examined the eating habits of 20 children at a nursery school. The variables measured for each child included: calories (the number of calories eaten at lunch), time (the time in minutes spent eating lunch), and sex (male=1, female=0). A multiple linear regression model using Y = calories, X1 = time, and X2 = sex led to the following model: y=547.65-2.85x1+10.67x2 For two children who spend the same amount of time eating, one male and one female, which child is predicted to consume more calories and by how much?
Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.016 ? = y intercept of population regression line = −7 Question: Graph the population regression line by first finding the point on the line corresponding to x = 1,000 and then the point corresponding to x = 2,000, and drawing a line through these points.
The following table gives the regression results of consumption behaviour between female and male. Consumption (C), in RM Model 1 Model 2 Constant 0.7515 0.6587 (0.024) (0.037) Y 0.8603 0.5442 (0.0301) (0.2881) Gen 0.2001 (0.0004) Y*Gen 0.3105 (0.0076) Adjusted R 0.78 0.78 No. of Observations 47 47 Note: Y=income (RM) Gen= Gender ( It is equal to 1 if person is female; 0 is for male) Figures in the parentheses are p- values a) Identify which are the qualitative, quantitative and interaction variable. Refer to Model 1: b) Write the regression equations for female and male. Draw the regression lines for female and male on the same diagram. What can you c) say? d) Interpret all the estimated slope coefficients. e) Conduct an appropriate test to determine whether variable gender is statistically significant at 5%. Should this variable be dropped from this regression model.
3. A study of beer consumption using the annual data from 1980 -2001 produced the following regression: Y = 0.41 +0.052.X₁; −0.047X2; +0.032X3; −0.018X4i (0.027) (0.011) (0.009) (0.008) (0.009) R² = 0.94 F = 66.58 DW statistic=1.32, figures in the brackets are standard errors Where: Y₁ = Annual aggregate beer consumption in year t (billion pints) X₁₁ = Real disposable income income in year t ($ billions at 2001 prices) X2i = Price of beer in year t (index number with 2001 = 100) X31 Price of wine and sprits in year t (index number with 2001 = 100) = X4₁ = Price of cigarettes in year t (index number 2001 = 100) (a) What is the effect of a change in the price of beer on beer consumption? Does it have the correct sign? Explain. (b) Comment on the signs of the other three coefficients. Are they as expected? (c) Tests the significance of the coefficients on each of the variables Xit i = 1, 2, 3, 4. What assumptions have you made in carrying out these tests? (d) What conclusion do you draw…
The percentage of adults who smoke in America is given below. Year America 1970 37.4 mon n 1980 33.2 1990 25.3 2000 23.1 2010 19.4 a) Write the linear regression model for A(x), representing the percentage of adult smokers in America x years since 1970. [Use your calculator OR Desmos to find the equation, Round coefficients to the nearest 100"] b) What is the slope of A(x)? Explain its meaning. c) Solve A(x) = 15. Show your work. Explain the meaning of your answer. d) Suppose in 2005, there were approximately 200 million adults in America. Use your model to estimate how many were smokers. Show how you get your answer.
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.
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…

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