The results from a regression analysis of data collected on SAT score and current GPA for a randomsample of 100 students at a large university are summarized in the partial computer output below.TermCoef SE CoefConstantSATr=0.4311.4060.1430.001340 0.000114R² = 0.1862Assume all conditions for inference were met. Based on the output shown, is there a statisticallysignificant linear relationship between SAT score and current GPA for all students at this university?(A) No, because the estimated slope is very close to 0.(B) No, because the correlation is not close to -1 or 1.(C) No, because R² is quite small.(D) Yes, because the ratio of 1.406 to 0.143 is very large.(E) Yes, because the ratio of 0.001340 to 0.000114 is very large.

The objective of the question is to determine if there is a statistically significant linear…

Answered: The results from a regression analysis…

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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Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables? (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly. (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly. (d) Suppose a second regression model (Model 2) was generated using only…
Managers of an outdoor coffee stand in Coast City are examining the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y , in dollars) and the maximum temperature (denoted by x , in degrees Fahrenheit) for each of fifteen randomly selected days during the past year are given below. These data are plotted in the scatter plot in Figure 1. Temperature, x(in degrees Fahrenheit) Coffee sales, y(in dollars) 53.1 2215.5 76.6 1982.7 70.1 1937.3 39.7 2251.1 72.5 1603.9 48.4 2024.2 46.7 2135.3 83.9 1536.5 58.4 1965.6 38.5 1944.3 68.2 1746.1 75.4 1472.1 65.6 1819.5 53.9 1627.4 45.1 1782.3 Send data to calculator Send data to Excel Coffee sales(in dollars) y 1200 1400 1600 1800 2000 2200 2400 x 40 50 60 70 80 90…
a) Compute the value of the sample correlation coefficient, r. (Round your answer to four decimal places.) r = b) Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t = P- value = c) If a regression analysis were to be carried out to predict endurance from lactate level, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.) ____________ d) If a regression analysis were to be carried out to predict lactate level from endurance, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.) _____________
Managers of an outdoor coffee stand in Coast City are examining the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y, in dollars) and the maximum temperature (denoted by x, in degrees Fahrenheit) for each of fifteen randomly selected days during the past year are given below. These data are plotted in the scatter plot in Figure 1. Also given is the product of the temperature and the coffee sales for each of the fifteen days. (These products, written in the column labelled "xy", may aid in calculations.) Temperature, X 10 Coffee sales, y (in dollars) (in degrees Fahrenheit) 37.2 51.3 59.7 53.7 63.1 44.5 47.5 75.9 82.2 40.0 74.8 70.6 69.0 48.3 74.7 Send data to calculator V 2000.4 2205.9 1944.8 1579.3 1846.3 1797.3 2016.5 1563.3 1556.5 2249.4 1653.9 1923.0 1747.9 2154.6 1979.7 74,414.88 113,162.67 116,104.56 84,808.41…
Consider the following computer output from a multiple regression analysis relating the cost of car insurance to the variables: number of car accidents, driver's credit score, and safety rating of the car. Intercept Car Accidents (In last 3 years) Credit Score Safety Rating Coefficients 1186 213.48 Coefficients - 130.46 294.11 Standard Error Does the sign of the coefficient for the variable safety rating make sense? 123.87 21.89 14.26 356.37 t Stat P-value 9.575 0.0000 9.752 0.0000 -9.149 0.0000 0.825 0.4128
A dog food company is interested in how much dog food a dog consumes based off of its weight. The company takes a random sample of dogs and finds that the best regression model to represent the data is as follows: Simple Linear Regression Results: Dependent Variable: Ounces of Food Consumed in a Week Independent Variable: Weight Food Consumed=-32.86 +5.25xWeight Sample Size: 500 R2:0.8129 Estimate of error standard deviation: 7.8563121 Suppose that a dog weighs 43.7 pounds, and typically eats 180 ounces of food per week. How many ounces of food would we predict the dog eats in a week, based on the least squares estimate? Provide your answer accurate to 1 digit past the decimal point. Answer: Suppose another dog weighs 20.1 pounds and consumes 70 ounces of food per week. What is the residual associate to this individual using the least squares estimate? Provide your answer accurate to 1 digit past the decimal point. Answer:
Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 80 mm Hg. Use a significance level of 0.05. Right Arm 100 99 93 77 77 Q Left Arm 174 168 148 148 146 Click the icon to view the critical values of the Pearson correlation coefficient r The regression equation is ŷ=+x. (Round to one decimal place as needed.) mm Hg. Given that the systolic blood pressure in the right arm is 80 mm Hg, the best predicted systolic blood pressure in the left arm is (Round to one decimal place as needed.) Data table Critical Values of the Pearson Correlation Coefficient r α = 0.05 α = 0.01 0.950 0.990 0.959 0.878 0.811 0.917 0.754 0.875 0.707 0.834 0.666 0.798 0.632 0.765 0.602 0.735 0.576 0.708 0.553 0.684 0.532 0.661 0.514 0.641 0.497 0.623 0.482…
A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x). The results of the regression were: ý=a+bx a=-1.692 b=0.117 (a) Write the equation of the Least Squares Regression line of the form (b) Which is a possible value for the correlation coefficient, r? O -0.649 O 1.32 O 0.649 O-1.32 (c) If a country increases its life expectancy, the happiness index will O increase O decrease (d) If the life expectancy is increased by 2.5 years in a certain country, how much will the happiness index change? Round to two decimal places. (e) Use the regression line to predict the happiness index of a country with a life expectancy of 75 years. Round to two decimal places.
The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of sixteen Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. The least-squares regression line for these data has equation Ŷ=42.80-0.53x. This line is shown in the scatter plot below. (The 2nd picture contains the rest of the data as it would not fit in the first pic and it includes the question as well.)
Let's study the relationship between brand, camera resolution, and internal storage capacity on the price of smartphones. Use α = .05 to perform a regression analysis of the Smartphones01CS dataset, and then answer the following questions. When you copy and paste output from MegaStat to answer a question, remember to choose to "Keep Formatting" to paste the text. a. Did you find any evidence of multicollinearity and variance inflation among the predictors. Explain your answer using a VIF analysis. b. Copy and paste the normal probability plot for your analysis. Is there any evidence that the errors are not normally distributed? Explain. c. Copy and paste the Residuals vs. Predicted Y-values. Does the pattern support the null hypothesis of constant variance for the errors? Explain. d. Study the residuals analysis. Which observations, if any, have unusual residuals? e. Study the residuals analysis. Calculate the leverage statistic. Which observations, if any, are high leverage…
Consider a certain data set on shoulder girth and height of a group of individuals. The mean shoulder girth is 107.20 cm with a standard deviation of 10.37 cm. The mean height is 171.14 cm with a standard deviation of 9.41 cm. The correlation between height and shoulder girth is 0.67. Calculate R2 of the regression line for predicting height from shoulder girth, and interpret it in the context of the application.
Consider the following computer output from a multiple regression analysis relating the cost of car insurance to the variables: number of car accidents, driver's credit score, and safety rating of the car. Coefficients Coefficients Standard Error t Stat P-value Intercept 956 97.23 9.832 0.0000 Car Accidents 172.08 18.24 9.434 0.0000 (In last 3 years) Credit Score Safety Rating 105.16 201.03 0.523 0.6030 -207.81 20.46 - 10.157 0.0000 Does the sign of the coefficient for the variable credit score make sense? Answer No, because it is expected that as the credit score increases then the cost should decrease. ○ No, because it is expected that as the credit score increases then the cost should also increase. ○ Yes, because it is expected that as the credit score increases then the cost should decrease. ○ Yes, because it is expected that as the credit score increases then the cost should also increase. Tables Keypad Keyboard Shortcuts

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