Math Problem Statement

Question content area top Part 1 Use the data set below to answer the following questions. Complete parts a through d. x 1x1 29 48 28 22 28 42 33 26 48 44

x 2x2 15 37 24 32 47 13 43 12 58 19 y 2020 4040 2929 2727 4141 1414 3535 1515 4141 1313 Question content area bottom Part 1 a. Obtain the estimated regression equation. ModifyingAbove y with caretyequals=nothing plus left parenthesis nothing right parenthesis x 1 plus left parenthesis nothing right parenthesis x 210.810.8+negative 0.1−0.1x1+0.70.7x2 ​(Round to one decimal place as​ needed.) Part 2 b. nbspb. Develop the correlation matrix for this set of data. Select the independent variable whose correlation magnitude is the smallest with the dependent variable. Determine if its correlation with the dependent variable is significant. Use alphaαequals=0.050.05. Complete the correlation matrix below. y x 1x1 x 2x2 y 1 x 1x1 0.1560.156 1 x 2x2 0.9160.916 0.2570.257 1 ​(Round to three decimal places as​ needed.) Part 3 Select the independent variable whose correlation magnitude is the smallest with the dependent variable. The parameter of interest is the population correlation coefficient between y and x 1x1 . Part 4 Determine the hypotheses. Choose the correct answer below. A. Upper H 0H0​: rhoρless than or equals≤0 Upper H Subscript Upper AHA​: rhoρgreater than>0 B. Upper H 0H0​: rhoρgreater than or equals≥0 Upper H Subscript Upper AHA​: rhoρless than<0 C. Upper H 0H0​: rhoρequals=0 Upper H Subscript Upper AHA​: rhoρnot equals≠0 Your answer is correct.D. Upper H 0H0​: rhoρnot equals≠0 Upper H Subscript Upper AHA​: rhoρequals=0 Part 5 Calculate the test statistic. tequals=enter your response here ​(Round to three decimal places as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Regression Analysis
Correlation Analysis
Hypothesis Testing
Multiple Linear Regression

Formulas

Regression Equation: y = b0 + b1x1 + b2x2
Correlation Coefficient: r = Cov(x, y) / sqrt(Var(x) * Var(y))
Test Statistic for Correlation: t = r * sqrt(n - 2) / sqrt(1 - r^2)

Theorems

Least Squares Method
Properties of Correlation Coefficients
Student's t-distribution for Hypothesis Testing

Suitable Grade Level

Undergraduate (Statistics or Econometrics)