A study of sales (Y ) with respect to x = advertising expenditure in a given retail business gave the following figures: n = 15, E Ti = 1,642.1,E Yi = 297.68, Er? = 179,858.72, E x; Yi = 32,314.27, E v? =6,440.66.If the equation of the least squares regression line is y = a + bx, then find the value of b. Give your answer to 3 decimal places.

Answered: Image /qna-images/answer/26443b56-3577-4906-80a5-742f07d970d2.jpg

Answered: A study of sales ( Y ) with respect to…

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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Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length. A least-squares regression on the data he collected produces the equation ŷ = 37.67 + 33.18x where x is metatarsal-to-femur ratio and y is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94. Construct a 96% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places. contact us help 6:42 PM povecy polcy terms of use careers A E O 4») 18 -క90.4 58 12/14/2020 a 17 |耳即 delets prt sc insert 112 19 18 + 16 backspace f5 fA
Suppose you are interested in studying the relationship between the number of visitors a museum gets and the revenue of their gift shop. You take a sample of 27 different days and record the number of visitors and the revenue of the gift shop in dollars. Also suppose on the 27 days you sampled, the number of visitors ranged from 100 people to 600 people. You get the following regression line: ŷ = 5.6x419, where ŷ is the revenue in dollars and x is the number of visitors. We also get that r≈.57. (a) Give the value of the slope of this regression line. Interpret this value in the context of the situation. (b) Is there enough evidence for a correlation? Why or why not? (c) What does our model predict the revenue will be on a day where the museum gets 1000 visitors? Would you trust this prediction? Why or why not? (d) Suppose that the first day we visited the museum it had 220 visitors and made a revenue of 780 dollars. Calculate the residual for this data point. Make sure to include…
4. Consider the following multiple regression results, where the dependent variable is the number of movie tickets sold per week, X, is the ticket price, and X2 is the cost of DVD rental. -51.0918X¡1 + 41.4607X¡2 (37.0184) (13.130) (0.584) Sp t = (-6.800) SSR = 17,023 SSE = 6,262 = 23,285 SST = п 3D 20 Complete the missing entries in the output. 1 | Are the slope coefficients, b, and b2, individually statistically significant (a = 0.10 2. 3. Calculate the standard error of the regression (s.) and the R2.
For major league baseball teams, do higher player payrolls mean more gate money? Here are data for each of the American League teams in the year 2002. The variable x denotes the player payroll (in millions of dollars) for the year 2002, and the variable y denotes the mean attendance (in thousands of fans) for the 81 home games that year. The data are plotted in the scatter plot below, as is the least-squares regression line. The equation for this line is y = 11.43 + 0.23x. Player payroll, x (in Mean attendance, y (in $1,000,000s) thousands) Anaheim 62.8 28.52 Baltimore 56.5 33.09 40- Boston 110.2 32.72 35 Chicago White Sox 54.5 20.74 30- Cleveland 74.9 32.35 25- Detroit 54.4 18.52 Kansas City 49.4 16.30 15- Minnesota 41.3 23.70 10+ New York Yankees 133.4 42.84 Oakland 41.9 26.79 20 40 60 80 100 120 140 Seattle 86.1 43.70 Player payroll, Тarmpa Bay 34.7 13.21 X (in $1,000,000s) Техas 106.9 29.01 Toronto 66.8 20.25 Send data to calculator Send data to Excel Based on the sample data and…
A recent study showed that the hours a person exercised in a week affected the individual'sresting heart rate. It was computed that r = -.68 and the least squares regression line was?̂ = 83-1.4x, where x is the hours exercised and y is the resting heart rate. d. What percentage of variability in resting heart rate can be explained by variability inhours exercised?
c) Show that the coefficient of determination, R², can also be obtained as the squared correlation between actual Y values and the Y values estimated from the regression model where Y is the dependent variable. Note that the coefficient of correlation between Y and X is Eyixi r = And also that ỹ = ŷ (18.75)
You are studying how a penguin's bill length (in mm) explains its body mass (in grams) using linear regression. You choose a non-directional alternative to be safe. Given the information below, choose the formula for the least squares regression line. b₁ = 87.42 bo = 362.31 x = 43.92 y = 4202.0 O Bill Length = 87.42 Body mass + 362.31 O Bill Length = 87.42*4202.0 + 362.31 O 4202.0 = 362.31*43.92 +87.42 O Body mass = 87.42 * Bill Length + 362.31 O Body mass = 362.31 *Bill Length + 87.42 O Body mass = 362.31 43.92 + 87.42
11. For temperature (x) and number of ice cream cones sold per hour (y). (65, 8), (70, 10), (75, 11), (80,13), (85, 12), (90, 16). Interpret the coefficient of determination. Optional Answers: 1. 88.2% of the variability in the number of cones sold is explained by the least-squares regression model. 2. 93.9% of the variability in the number of cones sold is explained by the least-squares regression model. 3. 88.2% of the variability in the temperature is explained by the least-squares regression model. 4. 93.9% of the variability in the temperature is explained by the least-squares regression model.

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