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....

...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...

...
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...

...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...

...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...

...Two important themes run through the study guide: data analysis and
decision making techniques.
Firstly we look at data analysis. This approach starts with data 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,...

...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...

...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...

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