Linear Regression Analysis: x vs y Data

Math Problem Statement

x values are 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19

y vaues 51.94, 52.38,48.12,45.46,44.8,42.04,38.48,35.12,32.36,32.5,26.34,26.98,25.02,21.66,17.4

Thank you for the clarification! I will now calculate the regression line for the updated $x$ and $y$ values.

The data provided is:

x & y \\ \hline 5 & 51.94 \\ 6 & 52.38 \\ 7 & 48.12 \\ 8 & 45.46 \\ 9 & 44.80 \\ 10 & 42.04 \\ 11 & 38.48 \\ 12 & 35.12 \\ 13 & 32.36 \\ 14 & 32.50 \\ 15 & 26.34 \\ 16 & 26.98 \\ 17 & 25.02 \\ 18 & 21.66 \\ 19 & 17.40 \\ \end{array}$$ I will compute the regression line now.# Updated data as per user input x_new = np.array([5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) y_new = np.array([51.94, 52.38, 48.12, 45.46, 44.80, 42.04, 38.48, 35.12, 32.36, 32.50, 26.34, 26.98, 25.02, 21.66, 17.40]) # Perform linear regression on the new data A_new = np.vstack([x_new, np.ones(len(x_new))]).T m_new, b_new = np.linalg.lstsq(A_new, y_new, rcond=None)[0] m_new, b_new # new slope and interceptThe updated equation of the regression line is: $$y = -2.49x + 65.87$$ Would you like further explanation on the steps, or have any other questions? Here are 5 additional questions to consider: 1. How can this regression line be used to predict $$y$$ for a new $$x$$ value? 2. What does the slope of $$-2.49$$ indicate about the relationship between $$x$$ and $$y$$? 3. How would you assess the accuracy of this regression model? 4. Can you calculate the residuals for each data point to check model fit? 5. What effect would removing extreme data points have on the regression line? **Tip:** The slope in a linear regression line tells you the rate of change. In this case, for each unit increase in $$x$$, $$y$$ decreases by approximately 2.49.

Drop file here or Click Here to upload

Linear Regression
Statistics

Linear regression formula: y = mx + b

Advanced High School

Linear Regression Analysis for Data Set with Scatterplot and Regression Line

Least-Squares Regression Line Calculation for Data Set

Regression Line Equation and Scatterplot Analysis

Linear Regression Line for Given Data Points

Linear Regression Equation and Residual Analysis for Data Set x = {-18, -15, -13, -12, -8} and y = {102, 122, 120, 132, 142}