An ice-cream vendor working at a holiday resort has a record of how many scoops of ice-cream he sold each day between 15 July and 20 August this year. He wonders whether his daily sales may depend on (1) the high temperature of the day (measured in "C) and (2) the day of the week. He collects data on daily high temperatures for this period from a meteorology website, and because he also has a deep interest in advanced statistical methods, he decides to fit a multiple linear regression model to the data to see whether sales can be reliably predicted form these two variables. The deterministic component of the model is hypothesised as E(y) = Bo + B₁x₁ + B₂x₂, where x₁ stands for the daily high temperature and x₂ is a dummy variable which equals 0 for weekdays (Monday to Friday) and 1 for weekends (Saturday and Sunday). The SPSS printout of the analysis is shown below. Model 1 Model R Square .256 212 a. Predictors: (Constant), Day of the week (x2), High temperature (x1) Model Summary R .506* Model Adjusted R Square Sum of Squares 276752.043 804838.307 1081590.350 ANOVA df Std. Error of the Estimate 153.856 Regression Residual Total a. Dependent Variable: Sales (scoops) b. Predictors: (Constant), Day of the week (x2), High temperature (x1) (Constant) High temperature (x1) Day of the week (x2) a. Dependent Variable: Sales (scoops) Mean Square 2 138376.022 34 23671.715 36 -212.093 15.713 118.233 Coefficients Unstandardized Coefficients Std. Error 195.196 5.906 54.039 Sig. 5.846 .007b Standardized Coefficients Beta 394 .324 1 -1.087 2.661 2.188 Sig. 285 012 .036 Find the estimated parameters and use the model to predict the number of scoops of ice-scream sold on a Wednesday when the high temperature is 30 °C. (Your answer must be accurate within +1
An ice-cream vendor working at a holiday resort has a record of how many scoops of ice-cream he sold each day between 15 July and 20 August this year. He wonders whether his daily sales may depend on (1) the high temperature of the day (measured in "C) and (2) the day of the week. He collects data on daily high temperatures for this period from a meteorology website, and because he also has a deep interest in advanced statistical methods, he decides to fit a multiple linear regression model to the data to see whether sales can be reliably predicted form these two variables. The deterministic component of the model is hypothesised as E(y) = Bo + B₁x₁ + B₂x₂, where x₁ stands for the daily high temperature and x₂ is a dummy variable which equals 0 for weekdays (Monday to Friday) and 1 for weekends (Saturday and Sunday). The SPSS printout of the analysis is shown below. Model 1 Model R Square .256 212 a. Predictors: (Constant), Day of the week (x2), High temperature (x1) Model Summary R .506* Model Adjusted R Square Sum of Squares 276752.043 804838.307 1081590.350 ANOVA df Std. Error of the Estimate 153.856 Regression Residual Total a. Dependent Variable: Sales (scoops) b. Predictors: (Constant), Day of the week (x2), High temperature (x1) (Constant) High temperature (x1) Day of the week (x2) a. Dependent Variable: Sales (scoops) Mean Square 2 138376.022 34 23671.715 36 -212.093 15.713 118.233 Coefficients Unstandardized Coefficients Std. Error 195.196 5.906 54.039 Sig. 5.846 .007b Standardized Coefficients Beta 394 .324 1 -1.087 2.661 2.188 Sig. 285 012 .036 Find the estimated parameters and use the model to predict the number of scoops of ice-scream sold on a Wednesday when the high temperature is 30 °C. (Your answer must be accurate within +1
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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Transcribed Image Text:An ice-cream vendor working at a holiday resort has a record of how many scoops of ice-cream he
sold each day between 15 July and 20 August this year. He wonders whether his daily sales may
depend on (1) the high temperature of the day (measured in °C) and (2) the day of the week. He
collects data on daily high temperatures for this period from a meteorology website, and because he
also has a deep interest in advanced statistical methods, he decides to fit a multiple linear regression
model to the data to see whether sales can be reliably predicted form these two variables. The
deterministic component of the model is hypothesised as E(y) = Bo + B₁x₁ + B₂x₂, where x₁
stands for the daily high temperature and x₂ is a dummy variable which equals 0 for weekdays
(Monday to Friday) and 1 for weekends (Saturday and Sunday). The SPSS printout of the analysis is
shown below.
Model
Model
R
.506*
Model Summary
R Square
256
212
a. Predictors: (Constant), Day of the week (x2), High
temperature (x1)
Model
Adjusted R
Square
Sum of
Squares
276752.043
804838.307
1081590.350
ANOVA
df
Std. Error of
the Estimate
153.856
Regression
Residual
Total
a. Dependent Variable: Sales (scoops)
b. Predictors: (Constant), Day of the week (x2), High temperature (x1)
(Constant)
High temperature (x1)
Day of the week (x2)
a. Dependent Variable: Sales (scoops)
Mean Square
2
138376.022
34 23671.715
36
-212.093
15.713
118.233
Coefficients
Unstandardized Coefficients
B
Std. Error
195.196
5.906
54.039
F
Sig.
5.846 .007b
Standardized
Coefficients
Beta
394
324
1
-1.087
2.661
2.188
Sig.
285
.012
.036
Find the estimated parameters and use the model to predict the number of scoops of ice-scream sold
on a Wednesday when the high temperature is 30 °C. (Your answer must be accurate within +1
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