2. Linear Modeling (Linear Regression) A bivariate (involving two variables) set of data is given in which x represents the number of police cars positioned along a freeway and y represents the average speed of cars on the freeway. X 2 7 12 16 a) Write the equation of the best-fit line. You may want to use the following formulas for the slope and y-intercept, respectively: m b N Σxy - Σx Σy N Σx2 – (Σx)2 y 70 65 47 32 Ex² Ey-Exy Ex N Σx2 – (Σ x)2 b) Assuming the best-fit line holds as an accurate model, what is the expected average speed of cars on the freeway if the number of police cars is 14? c) What is the correlation coefficient? Note: you can use the following equation for the correlation coefficient:

answer using minitab or excel

q4. Linear regression

The temperature of a liquid during the first four minutes of an experiment has been recorded in the table below. Time (x) (minutes) 0 1 2 3 4 Temperature (y) (°C) 30 33 40 56 73 Determine if the relationship between temperature and time is linear by constructing a residual plot.

Regression methods were used to analyze the data from a study investigating the relationship between roadway surface temperature (x) and pavement deflection (y). The simple linear regression model is y = 0.33 + 0.0042x. (a) Suppose that temperature is measured in °C rather than °F. Determine regression coefficients for the new model y = Bo +B1x. Round your answer to two decimal places (e.g. 98.76). Bo Round your answer to four decimal places (e.g. 98.7654). (b) What change in expected pavement deflection is associated with a 1°C change in surface temperature? Round your answer to four decimal places (e.g. 98.7654). Save for Later Attempts: 0 of 1 used Submit Answer

Lean body mass (weight leaving out fat ) helps predict metabolic rate (how many calories of energy are burned in a hour ) The relationship is roughly a straight line the least squares regression line for predicting metabolic rate (y in calories) from lean body mass (x in kilograms) is y =113.2+26.9x  The slope of regression line is ?

Statistics - Regression Analysis

Statistics professor wants to use the number of hours (x) a student studies for a statistics final exam to predict the final exam score (y). A regression model was fit based on data collected from a class during the previous semester, with the following results:                           (y hat): y   = 35.0 + 3X 1. What is the y-intercept?  2. What is the slope?  3. If the student spends 2 hours studying, what could be his/her final exam score? 4. If the student spends 2 hours studying, what could be his/her final exam score?5. If the student does not study for the final exam, what is the predicted final exam score?

How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms). x 3 6 12 20 26 y 60 95 140 160 189 (a) Make a scatter diagram of the data and visualize the line you think best fits the data.   Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website.   (b) Would you say the correlation is low, moderate, or strong?  low moderate     strong Would you say the correlation is positive or negative?  positive negative     (c) Use a calculator to verify that          x = 67,           x2 = 1265,           y = 644,           y2 = 93,546,  and          xy = 10,544.  Compute r. (Round your answer to three decimal places.)  As x increases from 3 to 26 months, does the value of r imply that y should tend to increase or decrease? Explain your answer.  Given our value of r, y should…

EQuestion Help Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below. Hours spent studying, x IA Test score,y 3 (a) x=2 hours (c) x= 12 hours (b) x = 25 hours (d) x= 4.5 hours 38 44 50 47 61 68 Find the regression equation. y = 6.269 x+ (32.48) (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) Choose the correct graph below. OD. OB. OC. O A. 80- 80- 80 80-4 0-+ Hours studying Hours studying Hours studying Hours studying 10 18 PM (E) More 10/3/2020 Click to select your answer(s)