Project 1 _multivariate statictics

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Durham College *

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DATA

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Statistics

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Apr 3, 2024

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docx

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Uploaded by JudgeBravery13371

Predictive Modelling with Linear Regression 1. Gathering Data I choosed "Adopted" dataset which contains 62 observations and 7 variables. Here is a breakdown of the dataset: Number of Observations: 62 Number of Variables: 7 Variables: 1. Age2IQ: This variable represents the IQ scores at age 2. It is a quantitative response variable containing numerical values that measure cognitive development. 2. Age4IQ: Similar to "Age2IQ," this variable represents IQ scores at age 4, a quantitative response variable. 3. Age8IQ: IQ scores at age 8, another quantitative response variable. 4. Age13IQ: IQ scores at age 13, yet another quantitative response variable. 5. BMIQ: This variable is likely related to Body Mass Index (BMI) at a specific age, which can be considered a quantitative predictor. 6. Origin: The "Origin" variable possibly indicating the source or origin of the data. Objective: The primary objective of analyzing the "Adopted" dataset is to investigate and model the relationship between the predictor variables (e.g., "BMIQ," other potential predictors) and the various quantitative response variables representing IQ scores at different ages (e.g., "Age2IQ," "Age4IQ," "Age8IQ," "Age13IQ"). The aim is to understand how these predictor variables influence cognitive development, as measured by IQ scores, at different stages of a person's life. 2. Initial Modelling I am choosing BMIQ as predictor and Age2IQ , Age4IQ , Age8IQ , Age13IQ as variable . In this part, I am exploring the relationship between "BMIQ" (Body Mass Index at a specific age) and different measures of IQ scores at different ages ("Age2IQ," "Age4IQ," "Age8IQ," and "Age13IQ") using linear regression and how 4 response variables are going to be affected by predictor . Summary :-

The above table shows min , 1 quartile , mean , median, 3 quartile, max. values . Correlations help to determine the strength and direction of the linear relationships between the two variables. Correlation between "BMIQ" and "Age2IQ” is 0.04211958 Correlation between "BMIQ" and "Age4IQ” is 0.2718603 Correlation between "BMIQ" and "Age8IQ” is 0.3620736 Correlation between "BMIQ" and "Age13IQ” is 0.3797961 Qus:- Run your regression in statistical software and report the coefficients in a well formatted table. 3. Diagnostics In this part of the analysis, I will perform diagnostic tests to assess whether linear regression holds and the impact of the "origin" variable on IQ scores at different ages. POINT PLOTS :- Adopted %>% ggplot(aes(x=BMIQ, y=Age2IQ+Age4IQ+Age8IQ+Age13IQ)) + geom_point()+ geom_smooth(method = "lm", se = FALSE)

From the above point graph it can be clearly seen that the linear regression between BMIQ predictor and Four response variables shows Positive regression. BOXPLOT:- origin: factor(origin) Adopted %>% ggplot(aes(x=factor(origin), y=Age2IQ)) + geom_boxplot() Adopted %>% ggplot(aes(x=factor(origin), y=Age4IQ)) + geom_boxplot() Adopted %>% ggplot(aes(x=factor (origin), y=Age8IQ)) + geom_boxplot() Adopted %>% ggplot(aes(x=factor(origin), y=Age13IQ)) + geom_boxplot()

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4. Model Selection firstModelIntelligence<- Adopted$BMIQ firstModelFitted <- Adopted$Age2IQ hist(firstModelIntelligence) qqnorm(firstModelResid) plot(firstModelFitted, firstModelIntelligence)

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5. Prediction and Summary To make predictions for the values provided in your BMIQ prediction data frame. Below are the predicted values for each input: Predicted BMIQ for input 1: 84.83007 Predicted BMIQ for input 2: 87.54676 Predicted BMIQ for input 3: 77.06197. Predicted BMIQ for input 4: 82.83206

The values show the model's estimated BMIQ scores for the corresponding combinations of Age2IQ and AMED provided in the BMIQ prediction data.