linear regression project

its a Linear regression project for Statistics and Probability.
can you please send me the step 1 selecting variables after finishing because i would send it to my instructor. and then then finish the rest by march 21st.

ANSWER

Linear Regression Project

Step 1: Selecting Variables

The selected variables comprise of weight (dependent) and height (independent) variable. The two variables are utilized in examining the application of linear regression to determine the impact of independent variable on the outcome. That is, the independent variables impact the outcome of the dependent variable. The measure or value of height as a variable can be used to determine the value of weight – dependent variable. This is often used to measure the body mass index (BMI) which is critical in maintaining balanced health standards.

The selection of weight and height variables will rely on the internet sources to guide the development of the data sets. Also, a recording of at least 30 values for each explanatory and response variables will be applied to examine the development of linear regression. The potential outcome is expected to show a strong linear regression relationship between height and weight of the recorded values.

The response variable entails of weight (dependent) whose values and outcome are influenced by the independent variable. The explanatory variable entails of height (independent) whose value is not affected by any other variable. There is a high likelihood that the height impacts on the weight positively. In the prospect where the weight exceeds the height, it shows a negative effect in the overall BMI analysis. Thus, there is a strong linear regression relationship between the two variables.

Step 2: Collecting the Data

The selected data set is indicated in the table 1 below. This comprises of numerous data sets provided to show the relation between weight and height. The data comprise of 36 data sets of varying points and values (Basker, 2018).

Table 1: Weight and Height Data Set.

NB: The selected dataset comprises of a list of weights and heaights that has been randomly collected and adjusted to look near to real standards health data.

Step 3: Visualizing the Data

Figure 1 below comprises of a scatter plot chart that assesses the relation between the two variables (weight and height). The scatter plot chart is used to determine whether the two variables seem to have a type of relationship that is analyzed below.

Figure 1: Weight and Height Scatter Plot.

The two variables (weight and height) show a type of positive linear relationship. That is, a certain change in the value of weight causes a similar change in the value of height. The two values influence each other in a positive manner. This indicates that the type of relationship experienced by the two variables is linear with a positive progression. Therefore, an increase in one value causes a direct positive impact on the other.

Step 4: Linear Regression

The calculation of correlation coefficient uses the formula indicated in the figure 2 below.

Equation (Schober, Boer & Schwarte, 2018).

Using a sample of five data set values selected from the table above, the correlation coefficient can be calculated as analyzed below.

The scatter plot chart for the above values.

Calculations

Key

X: X Values
Y: Y Values
Mx: Mean of X Values
My: Mean of Y Values
X – Mx & Y – My: Deviation scores
(X – Mx)2 & (Y – My)2: Deviation Squared
(X – Mx)(Y – My): Product of Deviation Scores

Result Details and Calculations

X Values
∑ = 225
Mean = 45
∑(X – Mx)2 = SSx = 61.54

Y Values
∑ = 736.6
Mean = 147.32
∑(Y – My)2 = SSy = 64.516

X and Y Combined
N = 5
∑(X – Mx)(Y – My) = 62.992

R Calculation
r = ∑((X – My)(Y – Mx)) / √((SSx)(SSy))

r = 62.992 / √((61.54)(64.516)) = 0.9997

Meta Numerics (cross-check)
r = 0.9997

Step 5: Analysis

The results above indicated that there is a strong positive correlation between the values of weight and height. The increment in the values of weight variable causes a subsequent effect on the values of height variable (and vice versa). The strong positive correlation where the value of R² (the coefficient of determination) is 0.9994 (close to 1) indicates that the two variables have linear regression (Schober et al., 2018).

The linear regression relationship between the weight and height selected from the sample data is an assertion of the increase of either value causes a similar effect on the other. It is integral to determine the two values must remain in constant linear regression relationship to maintain a healthy body. In the aspect where the height is much higher than the weight or vice versa, it indicates a contradiction in body balances. This posits the potential of body imbalances. For example, should the weight be too much higher than the height, it exposes an individual to the risk of developing health problems. Such include obesity, high blood pressure, among other weight related problems. Alternative, should the weight be too low as compared to the height of an individual shows malnutrition and underweight problems. The balancing of weight and height as the results of the correlation coefficient shows must maintain a positive result for a steady relationship. Therefore, there is a strong linear regression relationship between the height and weight of an individual. Thus, it is paramount for an individual to maintain steady growth and development in a balanced manner. Hence, result in the capacity of maintaining a steady growth and health of an individual.

References

Basker, J. (2018). Height_weight_single_variable_data_101_series_1.0: Predicting weight for a given height. Kaggle. Retrieved March 27, 2021, from https://www.kaggle.com/jamesbasker/height-weight-single-variable-data-101-series-10

Schober, P., Boer, C., & Schwarte, L. A. (2018). Correlation coefficients: appropriate use and interpretation. Anesthesia & Analgesia, 126(5), 1763-1768.