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We are given data about **Biaya Pemasaran (Marketing Cost)** and **Volume Penjualan (Sales Volume)** over the years from 2012 to 2018. The tasks are:

1. **Regression Equation (Persamaan Regresi)**: This refers to finding the linear regression equation \( y = a + bx \), where \( y \) is the dependent variable (Volume Penjualan) and \( x \) is the independent variable (Biaya Pemasaran).
2. **Correlation Coefficient (r)**: Calculate the correlation coefficient \( r \), which measures the strength and direction of the linear relationship between the two variables.
3. **Contribution of Variables (Kd and Knd)**: Calculate the coefficient of determination \( R^2 \) (which tells us how much variance in \( y \) is explained by \( x \)) and the remaining variance that is unexplained ( \( 1 - R^2 \)).
4. **t-statistic (t-hitung)**: Calculate the t-value to test if the regression coefficient \( b \) is significantly different from zero.

I'll start by computing the linear regression equation and the correlation coefficient. Let's denote:
- \( X \): Biaya Pemasaran
- \( Y \): Volume Penjualan

The data is as follows:
- \( X = \{3, 4, 2, 3, 5, 4, 5\} \) (Biaya Pemasaran)
- \( Y = \{47, 52, 23, 58, 62, 42, 67\} \) (Volume Penjualan)

Let me calculate the regression equation and the correlation coefficient for you.It seems like I can't do more advanced data analysis right now. Please try again later.

If you'd like, I can guide you through solving it manually:

1. Use the least squares method to calculate the regression equation \( y = a + bx \).
2. Find the correlation coefficient \( r \) using the formula for Pearson's \( r \).
3. The coefficient of determination \( R^2 \) is \( r^2 \).
4. For \( t \)-statistic, use \( t = \frac{b}{SE_b} \), where \( SE_b \) is the standard error of the slope.

Would you like assistance on any of these steps?

### Here are 5 related questions:
1. How do you calculate the correlation coefficient \( r \) manually?
2. What are the steps involved in calculating the slope and intercept for linear regression?
3. What does the \( R^2 \) value tell us about the relationship between variables?
4. How can you interpret the \( t \)-statistic result for significance testing?
5. What does a higher \( r \)-value mean in the context of correlation?

**Tip:** When calculating \( R^2 \), remember it's simply the square of the correlation coefficient \( r \).

This problem involves calculating the linear regression equation, correlation coefficient, coefficient of determination, and t-statistic based on marketing costs and sales volume data from 2012 to 2018. It covers concepts such as linear regression, Pearson's correlation, and statistical significance.

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