Curve fitting mcq
In this super long post, I cover Multiple Linear Regression describing briefly lol how it works and what criteria you need to take note of. So get yourself water and snacks, cause this will take a while. The bulk of the basic concepts were covered in my Simple Linear Regression posts, which can be found her e. The multiple linear regression explains the relationship between one continuous dependent variable y and two or more independent variables x 1, x 2, x 3… etc.
To find categorical variables e. Datasets to try your code on can be found everywhere. Kaggle also has real-life datasets. Note that in the wild, when you do encounter a dataset, it is going to be ugly AF. Due to the nature of the regression equation, your x variables have to be continuous as well. Continuous variables are simply put, running numbers. Categorical variables are categories.
It gets slightly confusing when your categorical variables appear continuous at first. For example, what if there was a column of zip codes or phone numbers? Every zip code represents a unique address and every phone number is just a unique contact number. Categorical Variables are also referred to as discrete or qualitative variables.
There are 3 types:. There are several ways to change a categorical data into continuous variables that can be used in regression. Your label should start at 0. Nominal and Ordinal variables are slightly more troublesome. Following the concept above, you label Red as 0, Blue as 1 and Grey as 2. When facing nominal variables that should not have different weightageone hot encoding is preferred. In order not to give categories that are on an even playing field any unequal values, we use one hot encoding.
For every level your variable is, just create a new x for each level. If your variable can only be 3 colours, then you should only be using 2 dummy variables. Grey becomes the reference category, in the case that your X blue and X red are both 0, then by default the variable would be Grey. Does it matter which variable you choose to exclude and use as a reference category? But the best practice would be to use the category that happens most often e. Does it make sense to hot encode different zip codes?
It is also absolutely pointless since every zip code is unique. It adds no insight to your model because how would you use such information to predict an outcome on new data?
If you need to predict the income level of someone living at zip codehow the heck would your model handle that if no such zip code was in your dataset? It has never seen this zip code before and cannot tell you anything about it.
What you can do is to transform it into something that you could be used to classify future data, such as grouping these zip codes by their areas this data would not be in the dataset but needs to be from domain knowledge or research. So instead of different zip codes, you get 4 regions, North, South, East or West OR depending on how specific you want to get, it could be actual areas like Hougang, Yishun, Bedok, Orchard etc.The model function, f x, …. It must take the independent variable as the first argument and the parameters to fit as separate remaining arguments.
The independent variable where the data is measured. Should usually be an M-length sequence or an k,M -shaped array for functions with k predictors, but can actually be any object. The dependent data, a length M array - nominally f xdata, Initial guess for the parameters length N. If None, then the initial values will all be 1 if the number of parameters for the function can be determined using introspection, otherwise a ValueError is raised. Determines the uncertainty in ydata. A 1-d sigma should contain values of standard deviations of errors in ydata.
A 2-d sigma should contain the covariance matrix of errors in ydata. T inv sigma r. If True, sigma is used in an absolute sense and the estimated parameter covariance pcov reflects these absolute values. If False, only the relative magnitudes of the sigma values matter. The returned parameter covariance matrix pcov is based on scaling sigma by a constant factor.Curve fitting in Python with curve_fit
This constant is set by demanding that the reduced chisq for the optimal parameters popt when using the scaled sigma equals unity. In other words, sigma is scaled to match the sample variance of the residuals after the fit.
If True, check that the input arrays do not contain nans of infs, and raise a ValueError if they do. Setting this parameter to False may silently produce nonsensical results if the input arrays do contain nans. Default is True. Lower and upper bounds on parameters. Defaults to no bounds. Each element of the tuple must be either an array with the length equal to the number of parameters, or a scalar in which case the bound is taken to be the same for all parameters.
Use np.Documentation Help Center. After fitting data with one or more models, you should evaluate the goodness of fit. A visual examination of the fitted curve displayed in Curve Fitting app should be your first step. Beyond that, the toolbox provides these methods to assess goodness of fit for both linear and nonlinear parametric fits:. Goodness-of-Fit Statistics. A particular application might dictate still other aspects of model fitting that are important to achieving a good fit, such as a simple model that is easy to interpret.
The methods described here can help you determine goodness of fit in all these senses. These methods group into two types: graphical and numerical. Plotting residuals and prediction bounds are graphical methods that aid visual interpretation, while computing goodness-of-fit statistics and coefficient confidence bounds yield numerical measures that aid statistical reasoning.
Generally speaking, graphical measures are more beneficial than numerical measures because they allow you to view the entire data set at once, and they can easily display a wide range of relationships between the model and the data. The numerical measures are more narrowly focused on a particular aspect of the data and often try to compress that information into a single number. In practice, depending on your data and analysis requirements, you might need to use both types to determine the best fit.
Note that it is possible that none of your fits can be considered suitable for your data, based on these methods. In this case, it might be that you need to select a different model. It is also possible that all the goodness-of-fit measures indicate that a particular fit is suitable.
However, if your goal is to extract fitted coefficients that have physical meaning, but your model does not reflect the physics of the data, the resulting coefficients are useless. In this case, understanding what your data represents and how it was measured is just as important as evaluating the goodness of fit.
After using graphical methods to evaluate the goodness of fit, you should examine the goodness-of-fit statistics.
For the current fit, these statistics are displayed in the Results pane in the Curve Fitting app. For all fits in the current curve-fitting session, you can compare the goodness-of-fit statistics in the Table of fits. Specify the gof output argument with the fit function.
This statistic measures the total deviation of the response values from the fit to the response values. It is also called the summed square of residuals and is usually labeled as SSE.
A value closer to 0 indicates that the model has a smaller random error component, and that the fit will be more useful for prediction. This statistic measures how successful the fit is in explaining the variation of the data. Put another way, R-square is the square of the correlation between the response values and the predicted response values.
It is also called the square of the multiple correlation coefficient and the coefficient of multiple determination.
SSR is defined as. Given these definitions, R-square is expressed as. R-square can take on any value between 0 and 1, with a value closer to 1 indicating that a greater proportion of variance is accounted for by the model. For example, an R-square value of 0. If you increase the number of fitted coefficients in your model, R-square will increase although the fit may not improve in a practical sense.Topics: Regression Analysis.
We often think of a relationship between two variables as a straight line. That is, if you increase the predictor by 1 unit, the response always increases by X units. However, not all data have a linear relationship, and your model must fit the curves present in the data. How do you fit a curve to your data? Fortunately, Minitab Statistical Software includes a variety of curve-fitting methods in both linear regression and nonlinear regression.
We want to accurately predict the output given the input. Here are the data to try it yourself! The most common way to fit curves to the data using linear regression is to include polynomial terms, such as squared or cubed predictors. Typically, you choose the model order by the number of bends you need in your line. Each increase in the exponent produces one more bend in the curved fitted line.
While the R-squared is high, the fitted line plot shows that the regression line systematically over- and under-predicts the data at different points in the curve. If your response data descends down to a floor, or ascends up to a ceiling as the input increases e. More generally, you want to use this form when the size of the effect for a predictor variable decreases as its value increases.
Looking at our data, it does appear to be flattening out and approaching an asymptote somewhere around I fit it with both a linear top and quadratic model bottom. For this particular example, the quadratic reciprocal model fits the data much better.
In the scatterplot below, I used the equations to plot fitted points for both models in the natural scale. The green data points clearly fall closer to the quadratic line. So far, this is our best model. A log transformation is a relatively common method that allows linear regression to perform curve fitting that would otherwise only be possible in nonlinear regression.
You can take the log of both sides of the equation, like above, which is called the double-log form. Or, you can take the log of just one side, known as the semi-log form. If you take the logs on the predictor side, it can be for all or just some of the predictors. Log functional forms can be quite powerful, but there are too many combinations to get into detail in this overview.
The choice of double-log versus semi-log for either the response or predictors depends on the specifics of your data and subject area knowledge. For data where the curve flattens out as the predictor increases, a semi-log model of the relevant predictor s can fit. Visually, we can see that the semi-log model systematically over and under-predicts the data at different points in the curve, just like quadratic model.
The S and R-squared values are also virtually identical to that model.
So far, the linear model with the reciprocal terms still provides the best fit for our curved data. Nonlinear regression can be a powerful alternative to linear regression because it provides the most flexible curve-fitting functionality. The trick is to find the nonlinear function that best fits the specific curve in your data. Fortunately, Minitab provides tools to make that easier. Next, click Use Catalog to choose from the nonlinear functions that Minitab supplies. We know that our data approaches an asymptote, so we can click on the two Asymptotic Regression functions.
The concave version matches our data more closely. Choose that function and click OK. Unlike linear regression, nonlinear regression uses an algorithm to find the best fit step-by-step.Notice: Visit gmstat. Question 1: The value of the coefficient of correlation lies between A 0 to 1 B 0 to -1 C -1 to 1 D 1 to Question 2: If the scatter diagram is drawn the scatter points lie on a straight line then it indicates a Skewness b Perfect correlation c No correlation d None of the above.
Question 6: The sample coefficient of correlation A Has the same sign as the slope, i. D Can range from A The line passes through the origin B The line passes through 5, 0 C The line is parallel to the y-axis D The line is parallel to the x-axis. This site uses Akismet to reduce spam. Learn how your comment data is processed.
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Statistics Assignment Help With Curve Fitting By Orthogonal Polynomial
Question 2. Question 3. Question 4. Question 4 Explanation:. Question 5. Question 6. Has the same sign as the slope, i. Question 7. Question 8. If the scatter diagram is drawn the scatter points lie on a straight line then it indicate.By what alternative name is Pearson's Correlation Analysis also known? Whether there is goodness of fit for one categorical variable Whether there is a relationship between variables Whether there is a significant effect and interaction of independent variables Whether there is a significant effect and interaction of dependent variables Whether there is a significant difference between groups Whether there is a significant difference between variables What type of data is required for a Pearson's analysis which does not include a dichotomous variable?
Interval or nominal Interval or ratio Nominal or ordinal Ordinal or interval Ratio or nominal Categorical or ratio What type of relationships does a Pearson's product-moment assess? It can only assess a linear relationship It finds differences not relationships Quadratic relationships Cubic relationships Curvilinear relationships Bi-modal relationships What must data be in order for a Pearson's product-moment to be conducted?
Homoscedasticity Parametric Normally distributed All of these Free from outliers Homogeneity of variance Homoscedasticity can be checked using which type of graph? Histogram Line graph Pie chart Bar chart Box-plot Scatter graph A bell shaped curve to a scatter graph would suggest what?
There would be a linear relationship and a Pearson's product-moment should be used There would be a linear relationship but a Pearson's product-moment should not be used There would be a non-linear relationship and a Pearson's product-moment should not be used There is an outlier but a Pearson's product moment can still be used There would be a non-linear relationship and a Pearson's product-moment should be used None of these If all points cluster in an ascending line this would suggest what?
There would be a weak positive relationship There would be a non-linear relationship There would be a strong negative relationship There would be no significant relationship There would be a weak negative relationship There would be a strong positive relationship If most points depict a dispersed descending line this would suggest what? There would be no significant relationship There would be a weak negative relationship There would be a non-linear relationship There would be a weak positive relationship There would be a strong positive relationship There would be a strong negative relationship How should a significance level of 0.
This would suggest strong negative relationship which is approaching significance This would suggest a strong, significant, positive relationship This would suggest strongsignificant, negative relationship This would suggest a weak negative relationship which is approaching significance This would suggest a weak, significant, positive relationship This would suggest a weak, non-significant, positive relationship When reporting a Spearman's Rho in APA format, what letter do you use to indicate which test you used?
It allows you to control covariates It allows you to use data which is not normally distributed It allows you to use dichotomous variables It allows you to use interval data None of these It allows you to use ratio data The Submit Answers for Grading feature requires scripting to function.
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SciPy | Curve Fitting
So, the Clear Answers and Start Over button below will not work. The following Clear Answers button is provided in its place and will clear your answers:. Student Resources. Multiple choice questions. Chapter 5: Multiple Choice Questions. None of these. Kruskal-Wallis Correlational Analysis. Pearson's Product-Moment.
Super Simple Machine Learning — Multiple Linear Regression Part 1
Mann-Whitney U Test. Spearman's Correlation Analysis. Chi-Squared Product-Moment. What does a Pearson's product-moment allow you to identify? Whether there is goodness of fit for one categorical variable. Whether there is a relationship between variables.
Whether there is a significant effect and interaction of independent variables. Whether there is a significant effect and interaction of dependent variables.
Whether there is a significant difference between groups. Whether there is a significant difference between variables. What type of data is required for a Pearson's analysis which does not include a dichotomous variable? Interval or nominal. Interval or ratio. Nominal or ordinal. Ordinal or interval. Ratio or nominal. Categorical or ratio.The negative value of the constant i.
The relatively low impact of the competitor's price c. The fact that not all of the variables are statistically significant d. The poor fit of the regression line. As the manager of Product A, which of the following would be of greatest concern based on the regression results above? None of the factors below would be of concern. An impending recession. Pressure on you by your salespersons to lower the price so that they can boost their sales.
A price reduction by the makers of product B. The ease of calculation. Relatively little analytical skill required. Its ability to provide information regarding the statistical significance of the results. All of the above. The solution gives answers to multiple choice questions on least squares estimation. The questions are related to regression equation, Student's t-test, least squares estimation, slope, intercept, correlation, residual, R square, coefficient of determination and regression coefficients.
Which of the Variables does NOT pass the t-test at the. All the variables pass the t-test 2. As a researcher, which aspect of the results would be of greatest concern? The poor fit of the regression line 3. Among the advantages of the least-squares trend analysis techniques is a. Add Solution to Cart Remove from Cart.