Example: Find the theoretical values for linear equation (y) from the given data a=0.0445, b=3.48, Sol: yi= a Xi + b Xi 6 8 10 12 14 16 18 20 22 24 Yi 3.8 3.7 4 3.9 4.3 4.2 4.2 4.4 4.5 4.5 yi 3.747 3.836 3.925 4.014 4.103 4.192 4.281 4.37 4.459 4.548
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. x 11.9 8.6 7.1 3.8 2.3 2.3 2.2 0.3 y 14.3 11 9.9 7.3 5.7 5.7 5.6 4.1 x = thousands of automatic weaponsy = murders per 100,000 residentsThis data can be modeled by the equation y=0.87x+3.75. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 5 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 10.5 thousand automatic weapons?Answer = Round to 3 decimal places.For which of the following models is y-hat = exp(b0 + b1x +se2/2) used to find the predicted value of y? Group of answer choices a. Y = b0 + b1x + eb. ln(y) = b0 + b1ln(x) + ec. y = b0 + b1ln(x) + ed. ln(y) = b0 + b1x + e
- To fit a simple linear regression model to the data and to provide its equation (d = a*t + b), along with R2 Day Date Weekday Daily Demand Weekend 1 4/25/2016 Mon 297 0 2 4/26/2016 Tue 293 0 3 4/27/2016 Wed 327 0 4 4/28/2016 Thu 315 0 5 4/29/2016 Fri 348 0 6 4/30/2016 Sat 447 1 7 5/1/2016 Sun 431 1 8 5/2/2016 Mon 283 0 9 5/3/2016 Tue 326 0 10 5/4/2016 Wed 317 0 11 5/5/2016 Thu 345 0 12 5/6/2016 Fri 355 0 13 5/7/2016 Sat 428 1 14 5/8/2016 Sun 454 1 15 5/9/2016 Mon 305 0 16 5/10/2016 Tue 310 0 17 5/11/2016 Wed 350 0 18 5/12/2016 Thu 308 0 19 5/13/2016 Fri 366 0 20 5/14/2016 Sat 460 1 21 5/15/2016 Sun 427 1 22 5/16/2016 Mon 291 0 23 5/17/2016 Tue 325 0 24 5/18/2016 Wed 354 0 25 5/19/2016 Thu 322 0 26 5/20/2016 Fri 405 0 27 5/21/2016 Sat 442 1 28 5/22/2016 Sun 454 1 29 5/23/2016 Mon 318 0 30 5/24/2016 Tue 298 0 31 5/25/2016 Wed 355 0 32 5/26/2016 Thu 355 0 33 5/27/2016 Fri 374 0 34 5/28/2016 Sat 447 1 35 5/29/2016…A chemistry experiment is performed measuring the solubility of potassium chloride (KCl) in water at different temperatures. The goal was to determine if there is a linear relationship between the temperature of the water and how much KCl can dissolve, measured as grams per 100 milliliter (g/100mL). After the experiments were performed, the following data was collected with temperature being the independent x-variable and solubility being the dependent y-variable: Temperature (°C) x Solubility (g/100mL) y 10 31 20 33 30 37 40 41 50 42 Based on the data given for temperature and solubility of KCl and without doing any math yet, which of the following do you predict would best describe the relationship between these variables? A positive linear relationship (r close to 1) A positive linear relationship (r close to -1) A negative linear relationship (r close to 1) A negative linear relationship (r close to -1)…28. Below is some of the regression output from a regression of the amount rental houses on an island rent for (expressed in thousands of $'s) based on the size of the house (expressed in square feet), whether the house has an ocean front view (VIEW = 1 if it has an ocean front view and = 0 if not), and an interaction term between the ocean front view dummy variable and the size of the house. If the estimated equation is:Price = 1,251 + 0.34*Size + 1,538*View + 0.07*(Size*View) Suppose you just built a house with an ocean front view that is 3600 square feet and you want to decide how much to rent it for. What is the predicted price of a house that is 3600 square feet and has an ocean front view? (please express your answer using 1 decimal places)
- Question 19: Based on the data shown below, a statistician calculates a linear model y=−2.23x+48.46y=-2.23x+48.46. x y 4 40.7 5 36.2 6 34.1 7 34.3 8 28.9 9 28.3 10 27.8 11 25.5 12 19.4 13 19.9 Use the model to estimate the y-value when x=4x=4y = Use the model to estimate the y-value when x=8x=8y =29. Below is some of the regression output from a regression of the amount rental houses on an island rent for (expressed in thousands of $'s) based on the size of the house (expressed in square feet), whether the house has an ocean front view (VIEW = 1 if it has an ocean front view and = 0 if not), and an interaction term between the ocean front view dummy variable and the size of the house. If the estimated equation isPrice = 1,444 + 0.3*Size + 1,411*View + 0.08*(Size*View) How much more (or less) does a 3800 square foot house that has an ocean front view rent for compared to a similar sized house without an ocean front view? (if the ocean front house rents for more then express your answer as a POSITIVE number; if the ocean front house rents for less then express your answer as a NEGATIVE number) (please express your answer using 1 decimal places)The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.4 8.2 6.9 3.4 2.5 2.6 2.1 0.7 yy 13.6 11.2 10 6.6 6.2 6.2 5.7 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.85x+4.05.y=0.85x+4.05. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 10 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 3.7 thousand automatic weapons?Answer = Round to 3 decimal places.
- Given are five observations for two variables, x and y. xi 3 12 6 20 14 yi 55 45 50 15 20 #1) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. y= #2) Use the estimated regression equation to predict the value of y when x = 13.Wh ich of the following regressions represents the weakest linear relationship between x and y? Regression 1y=ax+by=ax+ba=11.9a=11.9b=0.1b=0.1r=0.7944r=0.7944 Regression 2y=ax+by=ax+ba=12.9a=12.9b=19.8b=19.8r=0.0346r=0.0346 Regression 3y=ax+by=ax+ba=9.8a=9.8b=15.6b=15.6r=0.2439r=0.2439 Regression 4y=ax+by=ax+ba=-9.4a=−9.4b=11b=11r=-0.5893r=−0.5893 Regression }1Regression 1 t{Regression }2Regression 2 {Regression }3Regression 3 {Regression }4Regression 4