Coordinate AlgebraName: _____________________
4.2.3 ResidualsDate: _____________________
Introduction
The fit of a linear function to a set of data can be assessed by analyzing__________________. A residual is the vertical distance between an observed data value and an estimated data value on a line of best fit. Representing residuals on a___________________________ provides a visual representation of the residuals for a set of data. A residual plot contains the points: (x, residual for x). A random residual plot, with both positive and negative residual values, indicates that the line is a good fit for the data. If the residual plot follows a pattern, such as a U-shape, the line is likely not a good fit for the data. Key Concepts

* A residual is the distance between an observed data point and an estimated data value on a line of best fit. For the observed data point (x, y) and the estimated data value on a line of best fit (x, y0), the residual is y – y0. Day | Height in centimeters |

1 | 3 |
2 | 5.1 |
3 | 7.2 |
4 | 8.8 |
5 | 10.5 |
6 | 12.5 |
7 | 14 |
8 | 15.9 |
9 | 17.3 |
10 | 18.9 |
* A residual plot is a plot of each x-value and its corresponding residual. For the observed data point (x, y) and the estimated data value on a line of best fit (x, y0), the point on a residual plot is (x, y – y0). Guided Practice

Example 1
Pablo’s science class is growing plants. He recorded the height of his plant each day for 10 days. The plant’s height, in centimeters, over that time is listed in the table to the right.
Pablo determines that the function
y = 1.73x + 1.87 is a good fit for the
data. How close is his estimate to the
actual data? Approximately how
much does the plant grow each day?
1. Create a scatter plot of the data.

2. Draw the line of best fit through two
of the data points.

x | y = 1.73x + 1.87 |
1 | y = 1.73(1) + 1.87 = |
2 | y = 1.73(2)...

...
Simply use statistics as a tool. You will be given a data. (Next year you will not be given data, you will gather data yoruself).
1. Data: one of the variables is dependent and other dependent. Can be multiple. Then do regression analysis. ANOVA for overall significance and Regression equation. And write based on ANOVA there is a significance or not.
2. Some comments on correlation: volume vs. horse power etc.
3. Hypothesis test of one population. I assume that the mean is etc etc. Small paragraph analysis below the results of the test. ANOVA for small, large and medium size businesses for example.
Simply use statistics as a tool. You will be given a data. (Next year you will not be given data, you will gather data yoruself).
1. Data: one of the variables is dependent and other dependent. Can be multiple. Then do regression analysis. ANOVA for overall significance and Regression equation. And write based on ANOVA there is a significance or not.
2. Some comments on correlation: volume vs. horse power etc.
3. Hypothesis test of one population. I assume that the mean is etc etc. Small paragraph analysis below the results of the test. ANOVA for small, large and medium size businesses for example.
Simply use statistics as a tool. You will be given a data. (Next year you will not be...

...Trajico, Maria Liticia D.
BSEd III-A2
REFLECTION
The first thing that puffs in my mind when I heard the word STATISTIC is that it was a very hard subject because it is another branch of mathematics that will make my head or brain bleed of thinking of how I will handle it. I have learned that statistic is a branch of mathematics concerned with the study of information that is expressed in numbers, for example information about the number of times something happens. As I examined on what the statement says, the phrase “number of times something happens” really caught my attention because my subconscious says “here we go again the non-stop solving, analyzing of problems” and I was right. This course of basic statistic has provided me with the analytical skills to crunch numerical data and to make inference from it. At first I thought that I will be alright all along with this subject but it seems that just some part of it maybe it is because I don’t pay much of my attention to it but I have learned many things. I have learned my lesson.
During our every session in this subject before having our midterm examination I really had hard and bad times in coping up with this subject. When we have our very first quiz I thought that I would fail it but it did not happen but after that, my next quizzes I have taken I failed. I was always feeling down when in every quiz I failed because even though I don’t...

...
Data Analysis
Descriptive Statistics, Estimation, Regression & Correlation
Treatment Effects of a Drug on Cognitive Functioning in Children with Mental Retardation and ADHD
Hossam Elhowary
MATH-1016-15
Dr. Maria DeLucia
December 09, 2014
Introduction
The purpose of this survey was to investigate the cognitive effects of stimulant medication in children with mental retardation and Attention-Deficit/Hyperactivity Disorder. Twenty four children were given various dosage of a drug a placebo and 0.60mg/kg. Variable descriptions are kind of drug taken and the number of correct responses after taking of the drug. They were on each dose one week before testing. This sample obtained from the preschool delay task of Gordon Diagnostic System (Gordon, 1983). However, does higher dosage lead to higher cognitive performance?
Histogram:
Box-and-whisker plot:
Multi plot:
Summary statistics:
Column
n
Mean
Variance
Std. dev.
Std. err.
Median
Range
Min
Max
Q1
Q3
Placebo
24
39.75
128.02174
11.314669
2.3095972
36
45
26
71
33
47
0.60
24
44.708333
151.7808
12.319935
2.5147962
42.5
48
29
77
35
54
Simple linear regression results:
Dependent Variable: .60 mg/kg
Independent Variable: Placebo
.60 mg/kg = 10.091611 + 0.87086093 Placebo
Sample size: 24
R (correlation coefficient) = 0.79980157
R-sq = 0.63968255
Estimate of error standard deviation: 7.5614248
Parameter estimates:
Parameter
Estimate
Std. Err.
Alternative
DF
T-Stat...

...By: Chad R. Davis
23 May, 2012
Defining Statistical Data People rarely ever realize it; however, everyone has made some form of statistical statement or thought within their everyday life; from conversations to thinking about something. Take a puppy for example. For every month in age a puppy is equates to one hour of being able to hold their bladders (Humane Society, 2009). Other examples would be Survey Data’s that are fundamentally amalgamated into scopes of miscalculations, randomized sampling as well as certainty periods. Such thoughts like these are statistical by nature without us even realizing it. To further explain statistics, it is a discipline that is made up regarding certain factors that involve things like deductive reasoning; granted, Science is practically statistics in and of itself through fabricating experimentations that require data collectivity, recapitulating information for the purpose of understanding something and pulling deductions through the use of the Scientific Method (i.e. formulating theories) through data collection. Sample Data Sample data basically is a subclass of populations such as humans, animals and even objects; it often goes as far as Physical Science and the Scientific Method. Within statistics, known as survey methodology, Sample Data concerns itself in the selective method regarding the subset of...

...What are the characteristics of a population for which a mean/median/mode would be appropriate? Inappropriate?
The analysis of data begins with descriptive statistics such as the mean, median, mode, range, standard deviation, variance, standard error of the mean, and confidence intervals. These statistics are used to summarize data and provide information about the sample from which the data were drawn and the accuracy with which the sample represents the population of interest. The mean, median, and mode are measurements of the “central tendency” of the data. The range, standard deviation, variance, standard error of the mean, and confidence intervals provide information about the “dispersion” or variability of the data about the measurements of central tendency.
MEASUREMENTS OF CENTRAL TENDENCY The appropriateness of using the mean, median, or mode in data analysis is dependent upon the nature of the data set and its distribution (normal vs non-normal). The mean (denoted by x) is calculated by dividing the sum of the individual data points (where Σ equals “sum of”) by the number of observations (denoted by n). It is the arithmetic average of the observations and is used to describe the center of a data set.
mean=x= One of the most basic purposes of statistics is simply to enable us to make sense...

...than ever. Many organisations employ operations research or management science personnel or
consultants to apply the principles of scientiﬁc management to problems and decision making.
In this module we focus on a number of useful models and techniques that can be used in the
decision making process. Two important themes run through the study guide: data analysis and
decision making techniques.
Firstly we look at data analysis. This approach starts withdata that are manipulated or processed
into information that is valuable to decision making. The processing and manipulation of raw
data into meaningful information are the heart of data analysis. Data analysis includes data
description, data inference, the search for relationships in data and dealing with uncertainty
which in turn includes measuring uncertainty and modelling uncertainty explicitly.
In addition to data analysis, other decision making techniques are discussed. These techniques
include decision analysis, project scheduling and network models.
Chapter 1 illustrates a number of ways to summarise the information in data sets, also known as
descriptive statistics. It includes graphical and tabular summaries, as well as summary measures
such as means, medians and standard deviations.
Uncertainty is a key aspect of most business...

...μ=94.4
H₁: μ>94.4
Rejection Region:
Degree of freedom:
d.f=n-1
=49
t> ta,d.f
t>0.05,49
t>1.6766
Test statistics:
t=
From using the Data Analysis Plus in Excel we get:
t-Test: Mean
Cleanser Spending
Mean
102.4000
Standard Deviation
27.5711
Hypothesized Mean
94.4
df
49.0000
t Stat
2.0517
P(T1.6766).
2)
± ta/2,d.f s/
From using the Data Analysis Plus in Excel we get:
t-Estimate:Mean
Cleanser Spending
Mean
102.4000
Standard Deviation
27.5711
LCL
94.5645
UCL
110.2355
We estimate that the mean amount spent over one year lies between $94.56 and $110.26and when we divided by 4 we get the mean amount spent for every 3 month:
We estimate that the mean amount spent for every 3 month lies between $23.64 and $27.56. This estimate is 95% correct of the time
Case 2:
1)
Hypotheses:
H₀: μ=142
H₁: μ≠ 142
Rejection Region:
Degree of freedom:
d.f= n-1
=23
tta/2,d.f
tt0.05,23
t17139
Test statistic:
t=
From using the Data Analysis Plus in Excel we get:
t-Test: Mean
Hot Chocolate
Mean
141.3750
Standard Deviation
1.9959
Hypothesized Mean
142
df
23
t Stat
-1.5341
P(T9
Rejection Region:
Degree of freedom:
d.f= n-1
= 23
χ² > χ²a,d.f
χ² > χ² 0.1, 23
χ² > 32.0069
Test statistic:
χ²=
From using the Data Analysis Plus in...

...Random Sampling Method. In this case study, Mr Kwok collected a random sample of 1000 flights and proportions of three routes in the sample. He divides them into different sub-groups such as satisfaction, refreshments and departure time and then selects proportionally to highlight specific subgroup within the population. The reasons why Mr Kwok used this sampling method are that the cost per observation in the survey may be reduced and it also enables to increase the accuracy at a given cost.
TABLE 1: Data Summaries of Three Routes
Route 1
Route 2
Route 3
Normal(88.532,5.07943)
Normal(97.1033,5.04488)
Normal(107.15,5.15367)
Summary Statistics
Mean
88.532
Std Dev
5.0794269
Std Err Mean
0.2271589
Upper 95% Mean
88.978306
Lower 95% Mean
88.085694
N
500
Sum
44266
Summary Statistics
Mean
97.103333
Std Dev
5.0448811
Std Err Mean
0.2912663
Upper 95% Mean
97.676525
Lower 95% Mean
96.530142
N
300
Sum
29131
Summary Statistics
Mean
107.15
Std Dev
5.1536687
Std Err Mean
0.3644194
Upper 95% Mean
107.86862
Lower 95% Mean
106.43138
N
200
Sum
21430
From the table above, the total number of passengers for route 1 is 44,266, route 2 is 29,131 and route 3 is 21,430 and the total numbers of passengers for 3 routes are 94,827.
Although route 1 has the highest number of...