Question

Use SPSS to follow the steps below and conduct a simple linear regression of the following data:

Calories (Xi)	Sodium (Yi)
186	495
181	477
176	425
149	322
184	482
190	587
158	370
139	322
175	479
148	375

1. State your hypotheses (e.g. HA: “calories will significantly predict sodium”)

2. Create a scatterplot of the data. State if the scatterplot appears to contain a linear relationship.

3. Conduct the analysis in SPSS. Include all of the important outputs (e.g. ANOVA Table, Coefficient Table, Regression Table).

4. State your conclusion regarding the null hypothesis.

5. Write your conclusion. Include: (i) if there is a significant relationship between calories and sodium, based on the coefficient/slope, and (ii) if the model significantly predicts the sodium level, based upon adjusted R- squared.

6.

Use the results above to create the regression line equation (e.g. Yi = β1Xi + β0).

1. What numerical value is the slope (β1) associated with calories (Xi)?

2. What numerical value is the y-intercept (β0) associated with the regression line equation?

3. Write your regression line equation inserting the numerical slope value and y-intercept value (e.g. Yi = 0.75*Xi + 1.23)

4. Using the regression line equation from problem 5:

   1. What value is the (predicated) Yi, when Xi = 180?

   2. What value is the (predicated) Yi, when Xi = 155?

   3. What value is the (predicated) Yi, when Xi = 199?

Answer 1

Scatter Plot

From the scatter plot we observe that there is linear correlation between the two variable Sodium Calories.

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.933a	.871	.855	32.64527
a. Predictors: (Constant), Calories

2. Here from the Adjusted R square we observed that ,the model significantly predicts the sodium level.

ANOVAb
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	57524.691	1	57524.691	53.978	.000a
Residual	8525.709	8	1065.714
Total	66050.400	9
a. Predictors: (Constant), Calories
b. Dependent Variable: Sodium

1 . Here from the ANOVA table, we observed that

P value < alpha (level of Significance)

Hence we reject the null hypothesis and conclude that, calories will predict the sodium significantly.

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
B	Std. Error	Beta
1	(Constant)	-299.482	100.286		-2.986	.017
Calories	4.347	.592	.933	7.347	.000
a. Dependent Variable: Sodium

The numerical value is the slope (β1) associated with calories (Xi) is 4.347

The numerical value is the y-intercept (β0) associated with the regression line equation is -299.482

Line of regression equation,

Sodium (Y) = 4.347 * Calories – 299.482.

1. What value is the (predicated) Yi, when Xi = 180?

Sodium (Y) = 4.347 * Calories – 299.482.

Sodium (Y) = 4.347 * 180 – 299.482.

Sodium (Y) = 482.978

2. What value is the (predicated) Yi, when Xi = 155?

Sodium (Y) = 4.347 * Calories – 299.482.

Sodium (Y) = 4.347 * 155 – 299.482.

Sodium (Y) = 374.303.

3. What value is the (predicated) Yi, when Xi = 199?

Sodium (Y) = 4.347 * Calories – 299.482.

Sodium (Y) = 4.347 * 199 – 299.482.

Sodium (Y) = 565.571