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- An educator wants to see the number of absences(X) a student in her class has affects the Student's final GPA(Y) a) Find Correlation coefficiente b) Draw a Scatter plot (I c) Find the Regression equation of Y on X d) Predict the student's GPA when X = 6 X 4 5 2 8 3 10 7 y 2.5 2.3 4 2.1 3.3 1.7 2.3The annual consumer expenditures and annual net incomes of a sample of 7 families in Cambodia in 2020 are shown on the table below. Solve the following: 1. Correlational Analysis 2. Regression Analysis NET INCOME (x) IN EXPINDETURE (y) IN THOUSAND FAMILY HUNDRED THOUSAND PESOS PESOS A 15 В 15 7 C 3 18 D 16 14 E 17 26 F 18 22 G 11 4The price (in Tk.) and demand (in kg) of a product is given in the following table: Price (Tk.) 25 37 40 45 48 50 55 70 Demand (kg) 10 8 9 7.5 4.5 3 2 a. Determine the coefficient of correlation between the two variables. Answer rounded to three decimal places. b. Determine the slope coefficient B1 for the regression of Demand on Price. Answer rounded to three decimal places. c. Determine the y-intercept Bo for the regression of Demand on Price. Answer rounded to two decimal places. d. What will be the demand when price is Tk. 52? Answer rounded to two decimal places. LO
- When water flows across farmland, some soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (liters per second) on the amount of soil (kilograms) washed away. The data are given in the following table: Flow rate 0.31 0.85 1.26 2.47 3.75 Eroded soil 0.82 1.95 2.18 3.01 6.07 Let xx represent the flow rate variable and yy represent the variable for soil eroded. Then \bar x = 1.73, s_x = 1.38, \bar y = 2.81, s_y = 1.99xˉ=1.73,sx=1.38,yˉ=2.81,sy=1.99 Use this to complete the following calculation of the correlation coefficient for these data. r = \frac{1}{n-1}\left[\left(\frac{x_1 - \bar x}{s_x}\right)\left(\frac{y_1 - \bar y}{s_y}\right) + \left(\frac{x_2 - \bar x}{s_x}\right)\left(\frac{y_2 - \bar y}{s_y}\right) + \cdots + \left(\frac{x_n - \bar x}{s_x}\right)\left(\frac{y_n - \bar y}{s_y}\right)\right]r=n−11[(sxx1−xˉ)(syy1−yˉ)+(sxx2−xˉ)(syy2−yˉ)+⋯+(sxxn−xˉ)(syyn−yˉ)]…In a dataset, X is the independent variable, and Y is the dependent variable. Which of the following statement is correct? None of these Regression between X and Y determines the nature of the relationship between the variables. Regression between X and Y determines whether there exists any relationship between the variables. Correlation between X and Y determines the nature of the relationship between the variables.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.
- The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.8 8.4 7.2 3.6 2.7 2.7 2.2 0.7 yy 13.8 11.5 10 7.2 6.4 6.1 6.2 4.4 xx = thousands of automatic weaponsyy = murders per 100,000 residents This data can be modeled by the equation y=0.84x+4.06.y=0.84x+4.06. Use this equation to answer the following;A) How many murders per 100,000 residents can be expected in a state with 2.7 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 4.9 thousand automatic weapons?Answer = Round to 3 decimal places.Do a complete regression analysis using data below and find each item: a) Compute the value of the correlation coefficient. c) Use the Critical Value (CV) from the table to determine if there is a significant linear correlation. d) Determine the linear regression equation. e) Find the best predicted value.An educator wants to see the number of absences(X) a student in her class has affects the Student’s final GPA(Y)a) Find Correlation coefficient b) Draw a Scatter plot c) Find the Regression equation of Y on X d) Predict the student’s GPA when X = 6 x 4 5 2 8 3 10 7 y 2.5 2.3 4 2.1 3.3 1.7 2.3
- A departmental store has the following sales for a period of last one year of 8 salesmen, who have different years of education. Years of Education 8 10 10 12 14 16 Annual Sales (Thousand Tk.) 100 120 80 100 80 100 70 130 a. Determine the correlation coefficient r between the two variables. Answer rounded to at least 4 decimal places. b. Determine the slope coefficient B1 for the regression of annual sales on years of education. Answer rounded to at least 4 decimal places. c. Determine the y-intercept Bo for the regression of annual sales on years of education. Answer rounded to at least 4 decimal places. d. What will be the annual sales when the years of education is 11 (years)? Answer rounded to at least 4 decimal places. Thousand Tk.An economist was interested in the relation between the disposable income of a family and the amount of money used for food per month. He did a preliminary study on eight randomly selected lower income families. (Each family was of the same size; father, mother and two children). The economist’s data are given in the table below. Food cost (Y) (in hundreds of rand) 55 60 42 40 37 26 39 43 Family disposable income(X) (in hundreds of rand) 30 36 27 20 16 24 19 25 Find the regression linear equation. What is the predicted food cost if the family disposable income is R1800? Find the correlation coefficient & Interpret r. Find the Coefficient of Determination & Interpret the R2.In a regression study, relating Price/unit (x) to Weekly Sales (in Kg.), with the scatter plot showing a strong negative direction, 63% of the variability in sales could be accounted for by the variation in the Unit Price. The correlation coefficient in this study is: 0.79 -0.4 -0.79 0.4