Consider the following set of dependent and independent variables. Use these data to answer questions a and b in the photos below. y47444040272119159x12232181910188159x2716081554246321716a) construct a 95% confidence interval for the regression coefficient for x1 and interpret its meaning. -the 95% confidence interval for the true population b1 is ___ to ___. b) Construxt a 95% confidence interval for the regression coefficient for x2 and interpret its meaning. -the 95% confidence interval for the true population coefficient b2 is ___ to ___. Please help!! ## Constructing a 95% Confidence Interval for the Regression Coefficient### Task:b. Construct a 95% confidence interval for the regression coefficient for \( x_2 \) and interpret its meaning.### Information Provided:The 95% confidence interval for the true population coefficient \( \beta_2 \) is \[ \_\_\_ \] to \[ \_\_\_ \].*Note:* Round to three decimal places as needed.### Interpretation:Interpret the meaning of this confidence interval. Choose the correct answer below:- **A.** Since the confidence interval includes zero, there is sufficient evidence that \( \beta_2 \) is not zero, which indicates that there is a relationship between \( x_2 \) and \( y \).- **B.** Since the confidence interval does not include zero, there is insufficient evidence that \( \beta_2 \) is not zero, which indicates that there is not a relationship between \( x_2 \) and \( y \).- **C.** Since the confidence interval includes zero, there is insufficient evidence that \( \beta_2 \) is not zero, which indicates that there may not be a relationship between \( x_2 \) and \( y \).- **D.** Since the confidence interval does not include zero, there is sufficient evidence that \( \beta_2 \) is not zero, which indicates that there may be a relationship between \( x_2 \) and \( y \).### Instruction:Please click to select your answer(s). ### Understanding Confidence Intervals for Regression Coefficients#### Task:Construct a 95% confidence interval for the regression coefficient for \( x_1 \) and interpret its meaning.#### Solution:1. **Calculate the Confidence Interval**: The 95% confidence interval for the true population coefficient \( \beta_1 \) is from \([ \, \_\_ \, \text{ to } \, \_\_ \, ]\). (Round to three decimal places as needed.)2. **Interpret the Confidence Interval**: Choose the correct interpretation from the options below: - **A**: Since the confidence interval includes zero, there is insufficient evidence that \( \beta_1 \) is not zero, which indicates that there may not be a relationship between \( x_1 \) and \( y \). - **B**: Since the confidence interval does not include zero, there is sufficient evidence that \( \beta_1 \) is not zero, which indicates that there may be a relationship between \( x_1 \) and \( y \). - **C**: Since the confidence interval includes zero, there is sufficient evidence that \( \beta_1 \) is not zero, which indicates that there may not be a relationship between \( x_1 \) and \( y \). - **D**: Since the confidence interval does not include zero, there is insufficient evidence that \( \beta_1 \) is not zero, which indicates that there may not be a relationship between \( x_1 \) and \( y \).#### Explanation:A confidence interval for a regression coefficient gives a range of values within which we can say with a certain level of confidence (95% in this case) that the true coefficient lies. If the interval does not include zero, it suggests a statistically significant relationship. Conversely, if zero is included, the evidence for a relationship may be insufficient.

a. The regression analysis is conducted using EXCEL. The software procedure is given below: Enter the data. Select Data > Data Analysis >Regression> OK. Enter Input Y Range as A1:A10. Enter Input X Range as B1:C10. Mark Labels. Mark Confidence Level, enter 95%. Click OK. The output using EXCEL is as follows: From the output, the 95% confidence interval for the true population coefficient β1 is -0.216 to 1.345. Thus, the 95% confidence interval for the true population coefficient β1 is -0.216 to 1.345. Interpretation: The confidence interval for true population coefficient β1 contains the value 0. There would be insufficient evidence that β1 is not zero. This shows that, there might be no relation between the variables x1 and y. Correct answer: Option A. Since the confidence interval includes zero, there is insufficient evidence that β1 is not zero, which includes that there may not be a relationship between x1 and y.b. From the output, the 95% confidence interval for the true population coefficient β2 is 0.187 to 0.707. Thus, the 95% confidence interval for the true population coefficient β2 is 0.187 to 0.707. Interpretation: The confidence interval for true population coefficient β2 does not contain the value 0. There would be sufficient evidence that β2 is not zero. This shows that, there may be relation between the variables x2 and y. Correct answer: Option D. Since the confidence interval does not include zero, there is sufficient evidence that β2 is not zero, which includes that there may not be a relationship between x2 and y.