Skip to content
Solved Assignments

Linear Regression Analysis: Investigating Relationships Between Variables in Various Contexts

Examination of linear regression for analyzing variable relationships.

Preview 4 of 12 pages

See the first 4 pages exactly as they appear in the document.

  1. Page 1
    Read page 1 as text

    Linear Regression Analysis: Investigating Relationships Between Variables in Various Contexts Problem 1 The Mean Corporation has been commissioned to conduct a study is into the relationship between the population of a city and t he number of motor vehicle accidents in the city per year. A linear regression model is to be constructed. In the proposed regression model, number of motor vehicle accidents per year is the response variable and population of the city is the explanatory vari able. A random sample of 20 cities is selected and measurements are observed. Download the data Population ('000s) No. accidents per year 1,030 4,155 2,890 6,658 740 2,900 3,440 7,381 730 3,273 1,010 3,784 3,190 6,676 1,620 5,053 1,900 5,250 2,310 6,288 2,960 7,137 1,840 5,033 2,380 6,276 2,940 7,375 2,390 5,540 1,790 5,217 1,980 5,608 2,010 5,751 2,620 5,939 2,120 6,076 a) Calculate the point prediction for the value x = 2,500. Give your answer as a whole number. y ^ = 6197 b) Give the 95% prediction interval for the value x = 2,500. Give your answers as whole numbers.

  2. Page 2
  3. Page 3
    Read page 3 as text

    5429 ≤ y ^ ≤ 6966 Problem 2 An investigation has been conducted to determine whether there is a relationship between the salary paid to a Chief Executive Officer (CEO) and the productivity of that CEO as measured by the change in profits from the time the CEO was employed. The scatter plot plots the salary paid (x) against the change in profits (y) of a sample of CEOs. Without doing any calculations and according only to this scatter diagram, a reasonable coefficient of correlation (r) between x and y would be: r = - 1.25 r = - 0.59 r = 0.68 r = 1.35

  4. Page 4
    Read page 4 as text

    [2 points] - 3 of 11 ID: MST.SLR.REE.07.0020 Two variables (A and B) are hypothesised to have a linear relationship with one another, as represented by the following equation: A = β 0 + β 1 B + ε Data was gathered for these two variables and the correlation coefficient (r) was calculated to be - 0.96. Select all from the following statements that are true: The graph of the linear relationship between A and B slopes up. Variable A is known as the explanatory variable, and variable B is known as the response variable. The linear regression line provides a strong fit to the observed data. The proportion of variability in A that is explained by the regression model is equal to 92.16%. Causation between A and B cannot be implied from the correlation that exists between them. β 0 is known as the sample intercept. Variable B causes variable A since B is the independent variable.

8 more pages in the full document

Unlock it once and it stays in your library, ready to chat with or turn into flashcards.

Unlock the full document

More Statistics study materials

See all

Study this document with CramX

Once it is in your library, every tool can work from it.