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Help & explain please
Regression 1. A researcher is willing to investigate whether there is any linear relation bet ween income (x) in thousand dollars and food expenditures (y) in hundred dollars. A sample data on 7 households given the table below was collected. Assuming that a linear model is used to solve the problem. r-3-D) r-I 83 24 13 61 15 17 1. Write down the linear model 2. Write down the fitted regression line and Interpret the slope of this regression line. 3. What would be the expected food expenditures of an individual making about 55,000 dollars. Can we predict that of an individual making 95,000 dollars? why? 4. If somebody were to expend 1300 dollars, what would his earning income be? 2. In Brain and Beharior evolution (April 2000), Zoologists conducted a study of the feeding behavior of black-bream fish. The Zoologists recorded the number of aggressive strikes of black-bream fish feeding at the bottom of an aquarium in the 10-minute period following the addition of food. The next table lists the weekly number of strikes and age of the fish (in days). Assume that the line would be appropriate to fit this data. Week Number of Strikes Age of the fish (days) 136 150 155 162 169 178 184 190 34 35 57 12 15 (a) Write down the simple linear regression model that relates the number of strikes(t) to the age of the fish (x).
079 and regression analysis resulted in the following output : у regression line, r and r 19431-0.77, r- terpret the following: the estimated y-intercept, the slope of the fittecd is the average number of strikes of a fish with 165 days old? Can we predict that of a fish with 112 days old? Why? (d) What would be the age of a fish with 95 expected number of strikes? 3. An investigation of the properties of bricks used to line aluminum smelter plots was published bricks in the American Ceramic Society Bulletin (February 2005). Six different commercial were evaluated. The life length of a smelter plot depends on the porosity of the brick lining (the less porosity, the longer the life); consequently, the researchers measured the apparent porosity of each brick specimen, as well as the mean pore diameter of each brick. The data are given in the following table. Assume that the line would be appropriate to fit this data. Brick Apparent Porosity(6) Mean Pore Diameter (micrometers 18.0 18.3 16.3 6.9 17.1 20.4 12.0 9.7 7.3 5.3 16.8 (a) Write down the simple linear regression model that relates the apparent porosity (v) to (b) Find the fitted regression line. Interpret the estimated y-intercept and slope of the fitted (c) Predict the apparent porosity percentage for a brick with a mean pore diameter of 10 (d) What would be the mean pore dimeter of a brick with apparent porosity percentage of 4. A researcher at a large company has collected data on the beginning salary (x) and the the mean pore diameter (x). regression line. micrometers. Can we predict the one with mean pore diameter of 11 micrometers? Why? 25%? current salary () of 48 randomly selected employees. The least squares regression equation -2532.7 +2.12r. The current salaries had a mean of $32,070 with a standard deviation of $17,300. The begin- for predicting their current salary from their beginning salary is ning salaries had a mean of $16,340 with a standard deviation of $6,470. 1. What is the correlation (r) between current and beginning salary? What would you say about the strength and the direction of the linear association between z and y? 2. Compute r2 and give its interpretation.
Hint:-a + bz and b rs. 5. Real estate investors, homebuyers, and homeowners often use the appraised (or market) value r in thousand dollars) of a property as basis for predicting sale price (y in thousand dollars). From the data used in the analysis the market values range from $113,100 to $1,262,000, and the analysis results on the following plot with fitted regression line i - 1.36+1.41r, r-0.98 and r2 = 0.95. 8 8 (a) Based on the scatterplot, what can you say about the association between market value and sale price? (b) Interpret the slope of the fitted regression line, r and r2 (e) What would be the sale price for the market value of $145,000? Can we predict that of a market value of $80,000? Why ? (d) What would be the market value for a sale price of $500,000?
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