Question

When answering the question please explain the steps on how to form y=mx+b. I know how to make the graph, but im confused on how to calculate everything. thanks !

The data in the chart below is for the distance (in cm) to the near point, the point nearest the eye at which the eye can accurately focus, at a person's age. Near Point Age (years) (cm) 7.5 10 9 20 11.5 30 17.2 40 52.5 50 83.3 60 Make sure that you fill in each answer area before checking "How Did I Do?" Use a spreadsheet application to create a linear regression model for the data in the formy= y-intercept is where 0 years.) a. ma +b, where r is age and y is near point. (Hint: The Round each number in your model to two decimal places. y= Using your model, predict the near point of someone who is 80 years old. b. Round your answer to one decimal place. Number cm Do you think your linear model accurately represents the increase in near point based on age? Explain. C. EF T BIU A Equation Editor Σ Font Styles

Answer 1

Let X represent Age and Y represent Near Point We use the Excel Data Analysis Tool for Regression to get the regression equation Excel Menu->Data->Data Analysis->Regression We get the following summary data Coefficients a) Standard Error Near Point (Y) Age (X) -21.3533 14.7816 1.4720 0.3796 Here, Intercept Near Point Coefficient b -21.35 Age (X) coefficient = m and Slope 1.47 Thus, the regression equation is y mx +b y 1.47 x-21.35 b) Age X 80 years To predict Near Point Substitute value of X in the equation and find Y y 1.47 x-21.35 - 1.47 (80) 21.35 = 96.3 (Rounding to 1 decimal) Predicted Near Point 96.3 cm following summary fro for regression c) analysis Regression Statistics Here R-square is 0.7899 which 78.99%. Multiple R R Square Adjusted R Square Standard Error 0.888775432 This indicates that the variation in the value of 0.789921769 Near Point is correctly indicated 78.99% of the times 0.737402211 by this model 15.87798266 This indicates that the model is a good fit. 6 Observations ANOVA df ignificance SS MS Regression Residual Total 3791.872 3791.872 15.04053 1008.441333 252.1103 1 0.017868 4 4800.313333 Here, the Significance F value is 0.018, which is less than 5% Thus, at 5% level of significance, the regression is significant. Age (X) Line Fit Plot 100 80 60 Near Point (Y) АС Predicted Near Point (Y) 20 20 40 60 80 Age (X) The above line fit plot also shows a closeness of the actual near point and predicted near point Thus the linear model accurately indicates the increase in near point based on age Near Point (Y)