Given the following least-squares regression equation:\[\hat{y} = -13.586 + 4.340x\]where $ x $ represents the age of an elementary school student and $ y $ represents the score on a standardized test.**(a)** Interpret the value of the slope in this equation in the context of this data.**(b)** Give the $ y $-intercept, and explain why it does not make sense in this situation.**(c)** Use the regression equation to predict the score on this standardized test for a student who is 8 years old.**(d)** Use the regression equation to predict the age of a student who scores a 35 on the standardized test.---**Explanation of the Graph:**The graph visually represents the relationship between the age of elementary school students (x-axis) and their scores on a standardized test (y-axis). Each point on the scatter plot represents a student, plotting their age against their test score. A line of best fit, the least-squares regression line, is displayed, highlighting the linear relationship suggested by the data. This line follows the equation given: $\hat{y} = -13.586 + 4.340x$, indicating a positive correlation between age and score. As age increases, the score also tends to increase, as implied by the upward slope of the line. The graph includes data points primarily in the age range of 6 to 12 years and test scores ranging up to 40.

As per our guidelines, we are allowed to answer first three sub-parts only. Thanks a) The slope of…

Answered: Given the following least-squares…

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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A 1 ROAA (%) Efficiency Ratio (%) 2 1.04 39.93 3 57.75 4 81.4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0.68 7.27 1.08 0.72 0.92 0.79 1.04 1.76 1.07 1.37 0.93 0.66 1.72 1.5 0.59 2.12 1.11 1.45 1.06 B A 53.49 71.08 65.41 68.07 68.14 68.1 64.82 48.58 63.1 59.16 49.93 54.7 81.6 75.21 69.82 49.47 57.09 с Total Risk-Based Capital (%) 17.04 13.88 27.77 18.31 14.66 14.04 13.38 16.8 16.69 13.86 12 18.65 19.76 17.69 26.6 15.08 14.55 17.5 16.03 14.62 D E F G H |
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly Gross Revenue ($1,000s) 96 90 ŷ = 95 92 95 94 94 94 Television Newspaper Advertising Advertising ($1,000s) ($1,000s) 5.0 2.0 4.0 2.5 3.0 3.5 2.5 3.0 1.5 2.0 1.5 2.5 3.3 2.3 4.2 2.5 (a) Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let X₁ amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.) ŷ = represent the (b) Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s, x₂ represent the amount of newspaper advertising in $1,000s, and y represent the weekly…
The table shows the number of goals allowed and the total points earned (2 points for a win, and 1 point for an overtime or shootout loss) by 14 ice hockey teams over the course of a season. The equation of the regression line is y=−0.532x+211.813. Use the data to answer the following questions. (a) Find the coefficient of determination, r2, and interpret the result. (b) Find the standard error of the estimate, se, and interpret the result Goals Allowed, x Points, y215 112210 104217 103219 96259 85267 77281 51201 102214 99206 103216 94200 89263 70243 72
A statistical program is recommended. The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly Television Gross Newspaper Advertising Advertising ($1,000s) ($1,000s) Revenue ($1,000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5 1 (a) Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.) y = 88.64 + 1.60x1 X (b) Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s, x₂ represent the amount of…
An individual wants to determine how much money a boy scout earns from selling popcorn (Y-variable) based on the length of time (in days) that they went out selling (X-variable). Using the following linear regression equation Ŷ = 5 + 20X: a. State the value of the intercept AND the value of the slope (2 points) b. Based on the given regression equation, what can you determine about the direction of the relationship between X and Y (i.e. is it positive or negative)? (2 points) c. If a boy scout sells popcorn for 4 days, how much money is he predicted to earn? (2 points)
The admissions officer for a certain college developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high school GPA. ŷ = −1.39 + 0.0234x1 + 0.00482x2 where x1 = high-school grade point average x2 = SAT mathematics score y = final college grade point average. #1)A high-school average 84 corresponds to x1 = 84 and a score of 535 on the SAT mathematics test corresponds to x2 = 535. Substitute these values into the estimated regression equation to find the final college GPA, rounding the result to two decimal places. GPA = −1.39 + 0.0234x1 + 0.00482x2 = -1.39 +0.0234 (_____________) + 0.00482 (535) = __________________
The table shows the number of goals allowed and the total points earned (2 points for a win, and 1 point for an overtime or shootout loss) by 14 ice hockey teams over the course of a season. The equation of the regression line is y= - 0.558x + 216.186. Use the data to answer the following questions. (a) Find the coefficient of determination, r, and interpret the result. (b) Find the standard error of the estimate, s,, and interpret the result. Goals Allowed, x Points, y 218 212 216 220 257 266 274 200 211 206 216 204 264 244 O 111 106 99 90 86 83 45 105 100 101 94 83 67 68 (a) ? =O (Round to three decimal places as needed.)
Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southem U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow. Weekly Gross Revenue Television Advertising Newspaper Advertising ($100s) Market ($100s) ($100s) Mobile 102.5 5.1 1.6 Shreveport 52.7 3.2 3.0 Jackson 75.8 4.0 1.5 Birmingham 127.8 4.3 4.0 Little Rock 137.8 3.5 4.3 Biloxi 101.4 3.6 2.3 New Orleans 237.8 5.0 8.4 Baton Rouge 219.6 6.9 5.8 (a) Use the data to develop an estimated regression equation with the amount of television advertising as the independent variable. Let x represent the amount of television advertising. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) -43.258 O + 39.367 Test for a significant relationship between television advertising…
An oceanographer measured the length, in meters, of a deepwater wave and its speed, in meters per second. The results are shown in the following table. (a) Find the equation of a linear regression line for the data where wave length is the independent variable, x, and speed is the dependent variable. (Round your numerical values to two decimal places.) y= ? (b) Using the equation from part (a), estimate the speed (in meters per second) of a wave that is 200 m long. (Round your answer to one decimal place.) ? m/s
(d) Write out the regression equation. (Use 2 decimal places.) x1 = + x2 + x3 + x4 If x2 (production costs) and x4 (book sales) were held fixed but x3 (promotional costs) were increased by 0.7 million dollars, what would you expect for the corresponding change in x1 (box office receipts)? (Use 2 decimal places.)(e) Test each coefficient in the regression equation to determine if it is zero or not zero. Use level of significance 5%. (Use 2 decimal places for t and 3 decimal places for the P-value.) t P-value β2 β3 β4 (f) Find a 90% confidence interval for each coefficient. (Use 2 decimal places.) lower limit upper limit β2 β3 β4

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